Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22562404 | C2 | semidirect |
| 2. #22562387 | C2 | semidirect |
| 3. #22561632 | C2 | semidirect |
| 4. #22558221 | C2 | semidirect |
| 5. #22558218 | C2 | semidirect |
| 6. #22558133 | C2 | semidirect |
| 176. C67 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562404 | 2 |
| #22562387 | 2 |
| #22561632 | 2 |
| #22558221 | 2 |
| #22558218 | 2 |
| #22558133 | 2 |
| C67×#3191 | 2 |
| #12280 | 67 |