Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 95 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. #14546027 | C2 | semidirect |
| 2. #14545905 | C2 | semidirect |
| 5. #14545794 | C2 | semidirect |
| 6. #14545788 | C2 | semidirect |
| 59. C2×SD16×C17 | C8 | semidirect |
| 60. C2×#63230 | C8 | semidirect |
| 61. C2×#63229 | C8 | semidirect |
| 64. C2×#63219 | C8 | semidirect |
| 238. C2×SD16 | #3633 | semidirect |
| 274. C17 | #9090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14546027 | 2 |
| #14545905 | 2 |
| #14545904 | 2 |
| #14545898 | 2 |
| #14545794 | 2 |
| #14545788 | 2 |
| C2×#11763848 | 2 |
| #9090 | 17 |