Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 918 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×#10587499 | C2 | semidirect |
| 3. #14531041 | C2 | direct (N × H) |
| 4. C2×C4×#63214 | C2 | semidirect |
| 5. C2×C17×#494 | C2 | semidirect |
| 10. C2×#10587499 | C22 | semidirect |
| 14. C4×#63214 | C22 | semidirect |
| 19. C17×#494 | C22 | semidirect |
| 45. C2×#63214 | D4 | semidirect |
| 75. #63214 | C2×D4 | semidirect |
| 86. C2×C4×C17 | SD32 | semidirect |
| 100. C2×#494 | D17 | semidirect |
| 112. C4×C17 | C2×SD32 | semidirect |
| 125. #494 | C2×D17 | semidirect |
| 130. C2×C17 | #2248 | semidirect |
| 160. C17 | C2×#2248 | semidirect |
| 203. C2×C4 | #10587499 | semidirect |
| 220. C4 | C2×#10587499 | semidirect |
| 224. C2 | #14531041 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587499 | 2 |
| C2×#11763186 | 2 |
| #14531041 | 2 |
| C2×C4×#63214 | 2 |
| C2×C17×#494 | 2 |
| C2×#2248 | 17 |