Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
284 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14545802 | C2 | semidirect |
| 4. #14545801 | C2 | semidirect |
| 5. #14545800 | C2 | semidirect |
| 6. C8×#63241 | C2 | semidirect |
| 59. #63241 | M16 | semidirect |
| 90. C8×C17 | M32 | semidirect |
| 92. #3622 | M32 | semidirect |
| 153. C17 | #11409 | semidirect |
| 200. C8 | #10587670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545982 | 2 |
| C4×#10587670 | 2 |
| #14545802 | 2 |
| #14545801 | 2 |
| #14545800 | 2 |
| C8×#63241 | 2 |
| M16×#3624 | 2 |
| #11409 | 17 |