Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
108 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 35 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. #28414146 | C2 | semidirect |
| 2. #28414144 | C2 | semidirect |
| 3. C2×#20301486 | C2 | semidirect |
| 4. #28414126 | C2 | semidirect |
| 5. #28414053 | C2 | semidirect |
| 6. #28414034 | C2 | semidirect |
| 7. #100×C461 | C2 | semidirect |
| 53. C461 | #472 | semidirect |
| 61. #100 | D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414146 | 2 |
| #28414144 | 2 |
| C2×#20301486 | 2 |
| #28414126 | 2 |
| #28414053 | 2 |
| #28414034 | 2 |
| #100×C461 | 2 |
| #472 | 461 |