Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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. #14545649 | C2 | semidirect |
| 2. #14544085 | C2 | semidirect |
| 3. #14544085 | C2 | semidirect |
| 4. #14544025 | C2 | semidirect |
| 5. #14543624 | C2 | semidirect |
| 6. #14543610 | C2 | semidirect |
| 86. C2×D68 | M16 | semidirect |
| 100. C2×C8×C17 | M16 | semidirect |
| 262. C17 | #9093 | semidirect |
| 299. C2×C8 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545649 | 2 |
| #14544085 | 2 |
| #14544025 | 2 |
| #14543624 | 2 |
| #14543610 | 2 |
| C2×#11762920 | 2 |
| #9093 | 17 |