Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
280 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 280 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. #22562484 | C2 | semidirect |
| 3. #22562437 | C2 | semidirect |
| 5. #22559806 | C2 | semidirect |
| 7. C67×#1311 | C2 | semidirect |
| 68. C16×C67 | SD16 | semidirect |
| 110. #1311 | D67 | semidirect |
| 111. C67 | #12508 | semidirect |
| 172. C16 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562484 | 2 |
| #22562465 | 2 |
| #22562437 | 2 |
| #22562433 | 2 |
| #22559806 | 2 |
| #22559801 | 2 |
| C67×#1311 | 2 |
| #12508 | 67 |