Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 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. #14545978 | C2 | semidirect |
| 2. C2×C8×#3633 | C2 | semidirect |
| 3. #14545835 | C2 | semidirect |
| 4. #14545834 | C2 | semidirect |
| 8. #11763914 | C22 | semidirect |
| 11. C8×#3633 | C22 | semidirect |
| 41. C17×#135 | C8 | semidirect |
| 44. Q16×D17 | C8 | semidirect |
| 48. D8×D17 | C8 | semidirect |
| 49. #10587590 | C8 | semidirect |
| 98. Q16×C17 | C2×C8 | semidirect |
| 100. D8×C17 | C2×C8 | semidirect |
| 107. Dic68 | C2×C8 | semidirect |
| 108. D136 | C2×C8 | semidirect |
| 194. D17 | #1335 | semidirect |
| 201. #135 | #3633 | semidirect |
| 234. C17 | C2×#1335 | semidirect |
| 249. Q16 | C2×#3633 | semidirect |
| 256. D8 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545978 | 2 |
| C2×C8×#3633 | 2 |
| #14545835 | 2 |
| #14545834 | 2 |
| D17⋊#443 | 2 |
| C2×#1335 | 17 |