Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22569010 | C2 | semidirect |
| 2. C2×#16863206 | C2 | semidirect |
| 3. #22561925 | C2 | semidirect |
| 4. #22561086 | C2 | semidirect |
| 5. #22558315 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 24. #509×C67 | C4 | semidirect |
| 63. C2×D8×C67 | C2×C4 | semidirect |
| 69. M32×C67 | C2×C4 | semidirect |
| 106. Q16×C67 | C22⋊C4 | semidirect |
| 114. D8×C67 | C22⋊C4 | semidirect |
| 192. C67 | #13025 | semidirect |
| 197. #509 | Dic67 | semidirect |
| 226. C2×D8 | C2×Dic67 | semidirect |
| 244. M32 | C2×Dic67 | semidirect |
| 276. Q16 | C22⋊Dic67 | semidirect |
| 284. D8 | C22⋊Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569010 | 2 |
| C2×#16863206 | 2 |
| #22561925 | 2 |
| #22561086 | 2 |
| #22558315 | 2 |
| #22558292 | 2 |
| C2×#509×C67 | 2 |
| #13025 | 67 |