Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
134 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D67 |
| commutator, cosocle | C32×C67 | C23 |
| Frattini | C32 | C22×D67 |
| Fitting | C67×D64 | C2 |
| socle | C2×C67 | C2×D32 |
| hypercenter | D64 | D67 |
| hypocenter | C67 | #13742 |
| LCS | G ▷ C32×C67 ▷ C16×C67 ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22562515 | C2 | semidirect |
| 2. D32×D67 | C2 | semidirect |
| 3. #22558425 | C2 | semidirect |
| 4. #22558424 | C2 | semidirect |
| 5. #22558421 | C2 | semidirect |
| 6. #22558419 | C2 | semidirect |
| 7. C67×D64 | C2 | semidirect |
| 10. Dic1072 | C22 | semidirect |
| 15. C67⋊C64 | C22 | semidirect |
| 17. D32×C67 | C22 | semidirect |
| 18. C64×C67 | C22 | semidirect |
| 71. D64 | D67 | semidirect |
| 73. C67 | #13742 | semidirect |
| 81. D32 | C2×D67 | semidirect |
| 84. C64 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562515 | 2 |
| D32×D67 | 2 |
| #22558425 | 2 |
| #22558424 | 2 |
| #22558421 | 2 |
| #22558419 | 2 |
| C67×D64 | 2 |
| #13742 | 67 |