Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22562249 | C2 | semidirect |
| 3. #22559564 | C2 | semidirect |
| 4. #22558255 | C2 | semidirect |
| 5. #22558173 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 7. C67×#3287 | C2 | semidirect |
| 78. Q16×C67 | D8 | semidirect |
| 153. #3287 | 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 |
|---|---|
| #22562458 | 2 |
| #22562249 | 2 |
| #22559564 | 2 |
| #22558255 | 2 |
| #22558173 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#3287 | 2 |
| #12317 | 67 |