Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
238 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14543815 | C2 | semidirect |
| 4. #14543740 | C2 | semidirect |
| 6. #14543695 | C2 | semidirect |
| 36. C17×SD32 | C8 | semidirect |
| 54. Q16×C17 | C2×C8 | semidirect |
| 66. C16×C17 | C2×C8 | semidirect |
| 133. SD32 | #3624 | semidirect |
| 149. C17 | #12043 | semidirect |
| 154. Q16 | C2×#3624 | semidirect |
| 173. C16 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#3624 | 2 |
| D8×#3624 | 2 |
| #14543815 | 2 |
| #14543740 | 2 |
| #14543738 | 2 |
| #14543695 | 2 |
| SD32×Dic17 | 2 |
| #12043 | 17 |