Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#10587498 | C2 | semidirect |
| 2. C22×#10587497 | C2 | semidirect |
| 3. C2×#11763193 | C2 | semidirect |
| 4. #14531048 | C2 | direct (N × H) |
| 5. C2×#11762585 | C2 | semidirect |
| 6. C2×C17×#493 | C2 | semidirect |
| 12. C2×#10587498 | C22 | semidirect |
| 14. C2×#10587497 | C22 | semidirect |
| 17. #11763193 | C22 | semidirect |
| 18. #11762585 | C22 | semidirect |
| 23. C17×#493 | C22 | semidirect |
| 55. C2×#63214 | D4 | semidirect |
| 93. #63214 | C2×D4 | semidirect |
| 126. C2×#493 | D17 | semidirect |
| 158. #493 | C2×D17 | semidirect |
| 162. C2×C17 | #2250 | semidirect |
| 198. C17 | C2×#2250 | semidirect |
| 280. C2 | #14531048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587498 | 2 |
| C22×#10587497 | 2 |
| C2×#11763193 | 2 |
| #14531048 | 2 |
| C2×#11762585 | 2 |
| C2×C17×#493 | 2 |
| C2×#2250 | 17 |