Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
414 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 98 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. #14545123 | C2 | semidirect |
| 2. C8×#63242 | C2 | semidirect |
| 3. #14543747 | C2 | semidirect |
| 4. #14543746 | C2 | semidirect |
| 9. #11763731 | C22 | semidirect |
| 11. C8×#3624 | C22 | semidirect |
| 29. #10587605 | C8 | semidirect |
| 30. Q16×D17 | C8 | semidirect |
| 33. #10587598 | C8 | semidirect |
| 34. D8×D17 | C8 | semidirect |
| 76. Q16×C17 | C2×C8 | semidirect |
| 78. D8×C17 | C2×C8 | semidirect |
| 96. Dic68 | C2×C8 | semidirect |
| 97. D136 | C2×C8 | semidirect |
| 194. D17 | #1335 | semidirect |
| 234. C17 | C2×#1335 | semidirect |
| 249. Q16 | #63242 | semidirect |
| 256. D8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545123 | 2 |
| C8×#63242 | 2 |
| #14543747 | 2 |
| #14543746 | 2 |
| D17×#443 | 2 |
| C2×#1335 | 17 |