Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 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 | #30660725 |
| commutator, cosocle, hypocenter | C19×#3862 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C3×D3 |
| LCS | G ▷ C19×#3862 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22552727 | C2 | semidirect |
| 2. #30660725 | C2 | direct (N × H) |
| 3. C2×C19⋊#64418 | C3 | semidirect |
| 5. #22552727 | C22 | semidirect |
| 6. C2×C19×#3862 | C2×C3 | semidirect |
| 7. C2×#14584116 | D3 | semidirect |
| 9. C19⋊#64418 | C2×C3 | semidirect |
| 12. C19×#3862 | C22×C3 | semidirect |
| 13. #14584116 | C2×D3 | semidirect |
| 16. C2×C72×C19 | C3×D3 | semidirect |
| 22. C72×C19 | C2×C3×D3 | semidirect |
| 47. C2×#3862 | D19⋊C3 | semidirect |
| 61. #3862 | C2×D19⋊C3 | semidirect |
| 73. C2×C72 | C3⋊(D19⋊C3) | semidirect |
| 82. C72 | C2×C3⋊(D19⋊C3) | semidirect |
| 91. C2×C19 | #64418⋊C3 | semidirect |
| 102. C19 | C2×#64418⋊C3 | semidirect |
| 126. C2 | #30660725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552727 | 2 |
| #30660725 | 2 |
| C2×C19⋊#64418 | 3 |
| C2×#19150295 | 3 |
| C2×#64418⋊C3 | 19 |
| C2×C3⋊(D19⋊C3) | 49 |