Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
696 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 114 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. C22×#10587542 | C2 | semidirect |
| 2. #14544510 | C2 | semidirect |
| 3. C2×#11763665 | C2 | semidirect |
| 4. #14543660 | C2 | semidirect |
| 60. #10587542 | D4 | semidirect |
| 182. C22×C17 | #329 | semidirect |
| 275. C17 | #9119 | semidirect |
| 394. C22 | #11763665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587542 | 2 |
| #14544510 | 2 |
| C2×#11763665 | 2 |
| #14543660 | 2 |
| #14537087 | 2 |
| #9119 | 17 |