Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
282 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 64. Q16×C67 | Q16 | semidirect |
| 125. C67 | #12406 | semidirect |
| 177. Q16 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562489 | 2 |
| #22562351 | 2 |
| #22559603 | 2 |
| #22558267 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558173 | 2 |
| Q8×Q16×C67 | 2 |
| #12406 | 67 |