Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14529612 | C2 | semidirect |
| 3. #14527543 | C2 | semidirect |
| 4. #14527236 | C2 | semidirect |
| 5. C42×C8×C17 | C2 | semidirect |
| 7. #11763214 | C4 | semidirect |
| 8. #11763186 | C4 | semidirect |
| 9. #11763156 | C4 | semidirect |
| 67. C42×C17 | D8 | semidirect |
| 105. C8×C17 | #104 | semidirect |
| 109. C42×C8 | D17 | semidirect |
| 174. C17 | #9844 | semidirect |
| 202. C42 | D136 | semidirect |
| 233. C8 | #10587476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539363 | 2 |
| #14529612 | 2 |
| #14527543 | 2 |
| #14527236 | 2 |
| C42×C8×C17 | 2 |
| #9844 | 17 |