Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
252 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14531040 | C2 | semidirect |
| 2. #14528149 | C2 | semidirect |
| 4. #14526858 | C2 | semidirect |
| 5. #14526834 | C2 | semidirect |
| 6. #14526831 | C2 | semidirect |
| 7. D4×C16×C17 | C2 | semidirect |
| 73. C16×C17 | D8 | semidirect |
| 78. D4×C17 | SD32 | semidirect |
| 100. D4×C16 | D17 | semidirect |
| 163. C17 | #12432 | semidirect |
| 191. C16 | #63228 | semidirect |
| 202. D4 | #10587471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531040 | 2 |
| #14528149 | 2 |
| #14528139 | 2 |
| #14526858 | 2 |
| #14526834 | 2 |
| #14526831 | 2 |
| D4×C16×C17 | 2 |
| #12432 | 17 |