Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22558985 | C2 | semidirect |
| 3. #22558878 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558600 | C2 | semidirect |
| 6. #22558104 | C2 | semidirect |
| 7. C67×#1800 | C2 | semidirect |
| 185. #1800 | D67 | semidirect |
| 191. C67 | #10440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863591 | 2 |
| #22558985 | 2 |
| #22558878 | 2 |
| #22558600 | 2 |
| #22558104 | 2 |
| C67×#1800 | 2 |
| #10440 | 67 |