Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
156 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #30660690 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C9 |
| prime radical | C2×C7×D7×C19⋊C3 | C3 |
| cosocle | C72×C19⋊C3 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22552719 | C2 | semidirect |
| 2. #30660690 | C2 | direct (N × H) |
| 4. #22552719 | C22 | semidirect |
| 9. C2×C7×D7×C19 | C9 | semidirect |
| 16. C2×C72×C19 | C2×C9 | semidirect |
| 17. C7×D7×C19 | C2×C9 | semidirect |
| 24. C72×C19 | C22×C9 | semidirect |
| 35. C2×D7×C19 | C7⋊C9 | semidirect |
| 46. C2×C7×C19 | D7⋊C9 | semidirect |
| 47. C2×C7×C19 | C2×C7⋊C9 | semidirect |
| 48. D7×C19 | C2×C7⋊C9 | semidirect |
| 52. C2×C7×D7 | #4296 | semidirect |
| 56. C7×C19 | C2×D7⋊C9 | semidirect |
| 57. C7×C19 | C22×C7⋊C9 | semidirect |
| 65. C2×C72 | C2×#4296 | semidirect |
| 66. C7×D7 | C2×#4296 | semidirect |
| 74. C72 | C22×#4296 | semidirect |
| 81. C2×C19 | #11725076 | semidirect |
| 84. C2×D7 | #11924781 | semidirect |
| 88. C19 | C2×#11725076 | semidirect |
| 93. C2×C7 | #14558804 | semidirect |
| 94. C2×C7 | C2×#11924781 | semidirect |
| 95. D7 | C2×#11924781 | semidirect |
| 99. C7 | C2×#14558804 | semidirect |
| 100. C7 | C22×#11924781 | semidirect |
| 106. C2 | #30660690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552719 | 2 |
| #30660690 | 2 |
| C2×C7×D7×C19⋊C3 | 3 |
| C22×#11924781 | 7 |
| C2×#14558804 | 7 |
| C2×#11725076 | 19 |