Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
246 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 53. C67⋊C16 | Q16 | semidirect |
| 63. C16×C67 | Q16 | semidirect |
| 99. C67 | #12524 | semidirect |
| 155. C16 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562489 | 2 |
| #22562484 | 2 |
| #22562482 | 2 |
| #22559826 | 2 |
| #22559818 | 2 |
| #22558125 | 2 |
| C67×#2254 | 2 |
| #12524 | 67 |