Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22560985 | C2 | semidirect |
| 4. #22558881 | C2 | semidirect |
| 6. #22558059 | C2 | semidirect |
| 7. C2×#332×C67 | C2 | semidirect |
| 189. C2×#332 | D67 | semidirect |
| 192. C67 | #10550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570666 | 2 |
| #22560985 | 2 |
| #22558884 | 2 |
| #22558881 | 2 |
| #22558607 | 2 |
| #22558059 | 2 |
| C2×#332×C67 | 2 |
| #10550 | 67 |