Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 11. #11763898 | C4 | semidirect |
| 12. C8×#3633 | C4 | semidirect |
| 36. #10587533 | C8 | semidirect |
| 39. C17×#106 | C8 | semidirect |
| 40. #10587488 | C8 | semidirect |
| 41. #10587479 | C8 | semidirect |
| 89. #3633 | #106 | direct (N × H) |
| 101. C8×C17 | C4×C8 | semidirect |
| 102. #3622 | C4×C8 | semidirect |
| 155. #106 | #3633 | direct (N × H) |
| 166. C17 | C8×#106 | semidirect |
| 226. C8 | C4×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊C4×#3633 | 2 |
| C2×#11763898 | 2 |
| C2×C8×#3633 | 2 |
| #14545792 | 2 |
| #106×#595 | 2 |
| C8×#106 | 17 |