Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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×C22⋊(C67⋊C16) | C2 | semidirect |
| 2. #22560247 | C2 | semidirect |
| 3. #22558227 | C2 | semidirect |
| 4. #22558224 | C2 | semidirect |
| 173. C67 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C67⋊C16) | 2 |
| #22560247 | 2 |
| #22558227 | 2 |
| #22558224 | 2 |
| C67×#3050 | 2 |
| #11893 | 67 |