Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 76 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. Q16×#3624 | C2 | semidirect |
| 3. #14543818 | C2 | semidirect |
| 4. #14543740 | C2 | semidirect |
| 6. C16×#3624 | C2 | semidirect |
| 39. #10587499 | C8 | semidirect |
| 54. Q16×C17 | C2×C8 | semidirect |
| 67. #63214 | C2×C8 | semidirect |
| 86. #3624 | SD32 | semidirect |
| 149. C17 | C8×SD32 | semidirect |
| 154. Q16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#3624 | 2 |
| #14544365 | 2 |
| #14543818 | 2 |
| #14543740 | 2 |
| #14543739 | 2 |
| C16×#3624 | 2 |
| #14530633 | 2 |
| C8×SD32 | 17 |