Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
708 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 1. #14545925 | C2 | semidirect |
| 2. C2×(C2×#3633)⋊C4 | C2 | semidirect |
| 3. #14545785 | C2 | semidirect |
| 4. #14545783 | C2 | semidirect |
| 30. C2×#41×C17 | C8 | semidirect |
| 33. C2×#63256 | C8 | semidirect |
| 36. C2×#63254 | C8 | semidirect |
| 40. C2×#63252 | C8 | semidirect |
| 85. C2×Q8×C17 | C2×C8 | semidirect |
| 87. C2×D4×C17 | C2×C8 | semidirect |
| 107. C2×D68 | C2×C8 | semidirect |
| 120. C2×Dic34 | C2×C8 | semidirect |
| 286. C2×#41 | #3633 | semidirect |
| 318. C17 | #7578 | semidirect |
| 331. C2×Q8 | C2×#3633 | semidirect |
| 342. C2×D4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545925 | 2 |
| C2×(C2×#3633)⋊C4 | 2 |
| #14545785 | 2 |
| #14545783 | 2 |
| #14545245 | 2 |
| #7578 | 17 |