Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
3798 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 387 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. C2×#16863552 | C2 | semidirect |
| 3. #22560144 | C2 | semidirect |
| 6. C22×#11761618 | C22 | semidirect |
| 9. C2×#14523967 | C22 | semidirect |
| 55. C24×C67 | Q16 | semidirect |
| 104. C22×C67 | #451 | semidirect |
| 123. C67 | #32882 | semidirect |
| 164. C24 | #11761618 | semidirect |
| 222. C22 | #16863552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863552 | 2 |
| #22568496 | 2 |
| #22560144 | 2 |
| #22560119 | 2 |
| C24×Q8×C67 | 2 |
| #32882 | 67 |