Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 108. C4⋊C4×C67 | Q16 | semidirect |
| 188. C67 | #7783 | semidirect |
| 288. C4⋊C4 | Dic268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568162 | 2 |
| #22561542 | 2 |
| #22561538 | 2 |
| #22561311 | 2 |
| #22558034 | 2 |
| #22558033 | 2 |
| C67×#1271 | 2 |
| #7783 | 67 |