Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1080 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 213 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. #14545934 | C2 | semidirect |
| 2. #14545932 | C2 | semidirect |
| 3. #14545930 | C2 | semidirect |
| 4. #14545923 | C2 | semidirect |
| 6. C23×#3633 | C22 | semidirect |
| 7. C2×C4⋊#3633 | C22 | semidirect |
| 10. C2×C22⋊#3633 | C22 | semidirect |
| 11. C2×C4×#3633 | C22 | semidirect |
| 12. (C2×#3633)⋊C4 | C22 | semidirect |
| 42. C17×#120 | C8 | semidirect |
| 43. #10587639 | C8 | semidirect |
| 44. #10587623 | C8 | semidirect |
| 45. #10587568 | C8 | semidirect |
| 48. C24×C17 | C2×C8 | semidirect |
| 51. C23×D17 | C2×C8 | semidirect |
| 86. C22⋊C4×C17 | C2×C8 | semidirect |
| 87. C22⋊Dic17 | C2×C8 | semidirect |
| 88. #63227 | C2×C8 | semidirect |
| 191. #120 | #3633 | semidirect |
| 206. C17 | #23306 | semidirect |
| 212. C24 | C2×#3633 | semidirect |
| 245. C22⋊C4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545934 | 2 |
| #14545932 | 2 |
| #14545930 | 2 |
| #14545923 | 2 |
| #120×#595 | 2 |
| #23306 | 17 |