Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
674 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 674 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. #14544020 | C2 | semidirect |
| 3. C2×#11763652 | C2 | semidirect |
| 4. #14543627 | C2 | semidirect |
| 35. C17×#120 | C8 | semidirect |
| 58. C22⋊#3624 | D4 | semidirect |
| 71. C24×C17 | C2×C8 | semidirect |
| 103. C22⋊C4×C17 | C2×C8 | semidirect |
| 254. #120 | #3624 | semidirect |
| 283. C17 | #9107 | semidirect |
| 290. C24 | C2×#3624 | semidirect |
| 334. C22⋊C4 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545631 | 2 |
| #14544020 | 2 |
| C2×#11763652 | 2 |
| #14543627 | 2 |
| #14531445 | 2 |
| #9107 | 17 |