Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
272 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 83. Q16×C67 | Q16 | semidirect |
| 137. C67 | #12415 | semidirect |
| 196. Q16 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573174 | 2 |
| #22562492 | 2 |
| #22559724 | 2 |
| #22558260 | 2 |
| #22558190 | 2 |
| #22558179 | 2 |
| C67×#2227 | 2 |
| #12415 | 67 |