Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
702 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 3. C2×#11763734 | C2 | direct (N × H) |
| 11. #11763734 | C22 | direct (N × H) |
| 13. C2×#10587469 | C4 | semidirect |
| 15. C22×#63214 | C4 | semidirect |
| 16. C22×C16×C17 | C4 | semidirect |
| 34. C2×C16×C17 | C2×C4 | semidirect |
| 35. C2×#63214 | C2×C4 | semidirect |
| 36. #10587469 | C2×C4 | semidirect |
| 61. C16×C17 | C22×C4 | semidirect |
| 62. #63214 | C22×C4 | semidirect |
| 88. C22×C17 | #365 | semidirect |
| 105. C22×C16 | #595 | semidirect |
| 111. C2×C17 | C2×#365 | semidirect |
| 131. C2×C16 | C2×#595 | semidirect |
| 136. C17 | C22×#365 | semidirect |
| 161. C16 | C22×#595 | semidirect |
| 186. C22 | #11763734 | direct (N × H) |
| 195. C2 | C2×#11763734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587535 | 2 |
| C22×#10587533 | 2 |
| C2×#11763734 | 2 |
| C22×#10587469 | 2 |
| C22×#365 | 17 |