Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562496 | C2 | semidirect |
| 3. #22559727 | C2 | semidirect |
| 4. #22558261 | C2 | semidirect |
| 5. #22558191 | C2 | semidirect |
| 74. D8×C67 | Q16 | semidirect |
| 143. C67 | #12414 | semidirect |
| 205. D8 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562496 | 2 |
| #22562356 | 2 |
| #22559727 | 2 |
| #22558261 | 2 |
| #22558191 | 2 |
| #22558176 | 2 |
| C67×#3389 | 2 |
| #12414 | 67 |