Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 67 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×#3633 | C2 | semidirect |
| 3. #14545851 | C2 | semidirect |
| 4. #14545831 | C2 | semidirect |
| 6. C16×#3633 | C2 | semidirect |
| 42. C17×SD32 | C8 | semidirect |
| 43. #10587499 | C8 | semidirect |
| 44. #10587498 | C8 | semidirect |
| 45. #10587471 | C8 | semidirect |
| 64. Q16×C17 | C2×C8 | semidirect |
| 68. Dic68 | C2×C8 | semidirect |
| 72. C16×C17 | C2×C8 | semidirect |
| 73. #63214 | C2×C8 | semidirect |
| 86. #3633 | SD32 | direct (N × H) |
| 147. SD32 | #3633 | direct (N × H) |
| 163. C17 | C8×SD32 | semidirect |
| 169. Q16 | C2×#3633 | semidirect |
| 190. C16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#3633 | 2 |
| D8×#3633 | 2 |
| #14545851 | 2 |
| #14545831 | 2 |
| #14545830 | 2 |
| C16×#3633 | 2 |
| SD32×#595 | 2 |
| C8×SD32 | 17 |