Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
786 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 3. #14529339 | C2 | semidirect |
| 4. #14528645 | C2 | semidirect |
| 6. C42×#3622 | C2 | semidirect |
| 7. C17×#1839 | C2 | semidirect |
| 39. #10587562 | C8 | semidirect |
| 65. C42×C17 | C2×C8 | semidirect |
| 69. #63225 | C2×C8 | semidirect |
| 102. #3622 | #126 | semidirect |
| 106. #1839 | D17 | semidirect |
| 168. C17 | C8×#126 | semidirect |
| 196. C42 | C8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587562 | 2 |
| #14529388 | 2 |
| #14529339 | 2 |
| #14528645 | 2 |
| #14528554 | 2 |
| C42×#3622 | 2 |
| C17×#1839 | 2 |
| C8×#126 | 17 |