Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1734 conjugacy classes of subgroups; only the 510 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 510 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C67×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C43×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#492×C67 | C2 | semidirect |
| 2. C67×#2868 | C2 | semidirect |
| 4. C42×C8×C67 | C2 | semidirect |
| 24. C4×C8×C67 | D4 | semidirect |
| 36. C42×C67 | SD16 | semidirect |
| 48. C8×C67 | #127 | semidirect |
| 54. C4×C67 | #492 | semidirect |
| 56. #33300 | C67 | direct (N × H) |
| 60. C2×#492 | C2×C67 | semidirect |
| 61. #2868 | C2×C67 | semidirect |
| 63. C42×C8 | C2×C67 | semidirect |
| 64. C67 | #33300 | direct (N × H) |
| 84. C4×C8 | D4×C67 | semidirect |
| 96. C42 | SD16×C67 | semidirect |
| 108. C8 | #127×C67 | semidirect |
| 114. C4 | #492×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#492×C67 | 2 |
| C67×#2868 | 2 |
| C67×#2867 | 2 |
| C42×C8×C67 | 2 |
| #33300 | 67 |