Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
262 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562458 | C2 | semidirect |
| 2. #22562040 | C2 | semidirect |
| 3. #22559565 | C2 | semidirect |
| 4. #22559561 | C2 | semidirect |
| 5. #22558282 | C2 | semidirect |
| 6. #22558256 | C2 | semidirect |
| 7. C67×#1361 | C2 | semidirect |
| 63. C67⋊C16 | D8 | semidirect |
| 131. #1361 | D67 | semidirect |
| 132. C67 | #12433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562458 | 2 |
| #22562040 | 2 |
| #22559565 | 2 |
| #22559561 | 2 |
| #22558282 | 2 |
| #22558256 | 2 |
| C67×#1361 | 2 |
| #12433 | 67 |