Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
254 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 65 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. D8×#3633 | C2 | semidirect |
| 2. #14545851 | C2 | semidirect |
| 3. #14545830 | C2 | semidirect |
| 4. #14545799 | C2 | semidirect |
| 28. C17×D16 | C8 | semidirect |
| 29. #10587497 | C8 | semidirect |
| 30. D272 | C8 | semidirect |
| 43. D8×C17 | C2×C8 | semidirect |
| 45. D136 | C2×C8 | semidirect |
| 48. C16×C17 | C2×C8 | semidirect |
| 49. #63214 | C2×C8 | semidirect |
| 102. D16 | #3633 | semidirect |
| 113. C17 | #12045 | semidirect |
| 118. D8 | C2×#3633 | semidirect |
| 131. C16 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#3633 | 2 |
| #14545851 | 2 |
| #14545830 | 2 |
| #14545799 | 2 |
| D16×#595 | 2 |
| #12045 | 17 |