Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22562489 | C2 | semidirect |
| 3. #22562438 | C2 | semidirect |
| 5. #22559806 | C2 | semidirect |
| 6. C8×C67⋊C16 | C2 | semidirect |
| 54. C67⋊C16 | SD16 | semidirect |
| 85. C8×C67 | SD32 | semidirect |
| 111. C67 | #12505 | semidirect |
| 189. C8 | #14523987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562489 | 2 |
| #22562464 | 2 |
| #22562438 | 2 |
| #22562432 | 2 |
| #22559806 | 2 |
| C8×C67⋊C16 | 2 |
| C67×#1706 | 2 |
| #12505 | 67 |