Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14544365 | C2 | semidirect |
| 2. D8×#3624 | C2 | semidirect |
| 3. #14543818 | C2 | semidirect |
| 4. #14543739 | C2 | semidirect |
| 5. #14543738 | C2 | semidirect |
| 6. #14543695 | C2 | semidirect |
| 39. #10587497 | C8 | semidirect |
| 56. D8×C17 | C2×C8 | semidirect |
| 65. D136 | C2×C8 | semidirect |
| 68. #63214 | C2×C8 | semidirect |
| 155. C17 | #12045 | semidirect |
| 163. D8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544365 | 2 |
| D8×#3624 | 2 |
| #14543818 | 2 |
| #14543739 | 2 |
| #14543738 | 2 |
| #14543695 | 2 |
| #14530628 | 2 |
| #12045 | 17 |