Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1022 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 251 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×#10587497 | C2 | semidirect |
| 2. C2×#11763186 | C2 | semidirect |
| 3. #14531033 | C2 | direct (N × H) |
| 4. C2×C4×#63214 | C2 | semidirect |
| 5. C2×C17×#493 | C2 | semidirect |
| 10. C2×#10587497 | C22 | semidirect |
| 13. #11763186 | C22 | semidirect |
| 14. C4×#63214 | C22 | semidirect |
| 19. C17×#493 | C22 | semidirect |
| 45. C2×#63214 | D4 | semidirect |
| 76. #63214 | C2×D4 | semidirect |
| 89. C2×C4×C17 | D16 | semidirect |
| 104. C2×#493 | D17 | semidirect |
| 117. C4×C17 | C2×D16 | semidirect |
| 132. #493 | C2×D17 | semidirect |
| 136. C2×C17 | #2246 | semidirect |
| 166. C17 | C2×#2246 | semidirect |
| 212. C2×C4 | #10587497 | semidirect |
| 231. C4 | C2×#10587497 | semidirect |
| 236. C2 | #14531033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587497 | 2 |
| C2×#11763186 | 2 |
| #14531033 | 2 |
| C2×C4×#63214 | 2 |
| C2×C17×#493 | 2 |
| C2×#2246 | 17 |