Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
630 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 124 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. #14545631 | C2 | semidirect |
| 2. #14544083 | C2 | semidirect |
| 3. #14544024 | C2 | semidirect |
| 4. #14543608 | C2 | semidirect |
| 28. C17×#127 | C8 | semidirect |
| 48. C4×#3624 | D4 | semidirect |
| 63. C2×D4×C17 | C2×C8 | semidirect |
| 81. C42×C17 | C2×C8 | semidirect |
| 191. #127 | #3624 | semidirect |
| 215. C17 | #9101 | semidirect |
| 227. C2×D4 | C2×#3624 | semidirect |
| 255. C42 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545631 | 2 |
| #14544083 | 2 |
| #14544024 | 2 |
| #14543608 | 2 |
| #14531510 | 2 |
| #9101 | 17 |