Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22571968 | C2 | semidirect |
| 2. #22562458 | C2 | semidirect |
| 3. #22559561 | C2 | semidirect |
| 4. #22558256 | C2 | semidirect |
| 5. #22558173 | C2 | semidirect |
| 6. #22558163 | C2 | semidirect |
| 7. C67×#2207 | C2 | semidirect |
| 84. Q16×C67 | D8 | semidirect |
| 155. #2207 | D67 | semidirect |
| 160. C67 | #12317 | semidirect |
| 224. Q16 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571968 | 2 |
| #22562458 | 2 |
| #22559561 | 2 |
| #22558256 | 2 |
| #22558173 | 2 |
| #22558163 | 2 |
| C67×#2207 | 2 |
| #12317 | 67 |