Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 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×D272 | C2 | semidirect |
| 2. C22×#10587497 | C2 | semidirect |
| 3. C2×#11763184 | C2 | semidirect |
| 4. #14531032 | C2 | direct (N × H) |
| 5. C2×C16×Dic17 | C2 | semidirect |
| 6. C22×C17×D16 | C2 | semidirect |
| 11. C2×D272 | C22 | semidirect |
| 13. C2×#10587497 | C22 | semidirect |
| 16. #11763184 | C22 | semidirect |
| 18. C16×Dic17 | C22 | semidirect |
| 21. C2×C17×D16 | C22 | semidirect |
| 42. C2×C16×C17 | D4 | semidirect |
| 47. C2×#63214 | D4 | semidirect |
| 79. C16×C17 | C2×D4 | semidirect |
| 80. #63214 | C2×D4 | semidirect |
| 97. C2×Dic17 | D16 | semidirect |
| 108. C22×D16 | D17 | semidirect |
| 124. Dic17 | C2×D16 | semidirect |
| 134. C2×D16 | C2×D17 | semidirect |
| 142. C2×C17 | #2246 | semidirect |
| 169. C2×C16 | C22⋊D17 | semidirect |
| 173. C17 | C2×#2246 | semidirect |
| 204. C16 | C2×C22⋊D17 | semidirect |
| 244. C2 | #14531032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| C22×#10587497 | 2 |
| C2×#11763184 | 2 |
| #14531032 | 2 |
| C2×C16×Dic17 | 2 |
| C22×C17×D16 | 2 |
| C2×#2246 | 17 |