Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
930 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 235 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×#10587471 | C2 | semidirect |
| 2. C22×D272 | C2 | semidirect |
| 3. C2×#11763193 | C2 | semidirect |
| 4. C2×#11763186 | C2 | semidirect |
| 5. #14531050 | C2 | direct (N × H) |
| 6. C2×C17×#346 | C2 | semidirect |
| 15. C2×#10587471 | C22 | semidirect |
| 17. C2×D272 | C22 | semidirect |
| 19. #11763193 | C22 | semidirect |
| 21. #11763186 | C22 | semidirect |
| 24. C17×#346 | C22 | semidirect |
| 51. C2×C16×C17 | D4 | semidirect |
| 93. C16×C17 | C2×D4 | semidirect |
| 128. C2×#346 | D17 | semidirect |
| 160. #346 | C2×D17 | semidirect |
| 161. C2×C17 | #2250 | semidirect |
| 194. C2×C16 | D68 | semidirect |
| 198. C17 | C2×#2250 | semidirect |
| 235. C16 | C2×D68 | semidirect |
| 280. C2 | #14531050 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587471 | 2 |
| C22×D272 | 2 |
| C2×#11763193 | 2 |
| C2×#11763186 | 2 |
| #14531050 | 2 |
| C2×C17×#346 | 2 |
| C2×#2250 | 17 |