Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
242 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22562041 | C2 | semidirect |
| 2. D4×C67⋊C16 | C2 | semidirect |
| 3. #22558273 | C2 | semidirect |
| 4. D4⋊(C67⋊C16) | C2 | semidirect |
| 5. D4⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558127 | C2 | semidirect |
| 76. D4×C67 | M32 | semidirect |
| 121. C67 | #12063 | semidirect |
| 190. D4 | #14523983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562041 | 2 |
| D4×C67⋊C16 | 2 |
| #22558273 | 2 |
| D4⋊(C67⋊C16) | 2 |
| #22558127 | 2 |
| C8×D8×C67 | 2 |
| #12063 | 67 |