Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 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. C22×#16864513 | C2 | semidirect |
| 2. C2×C8×D541 | C2 | semidirect |
| 4. #31772557 | C2 | semidirect |
| 5. #31772540 | C2 | semidirect |
| 6. C8×Dic541 | C2 | semidirect |
| 7. C22⋊C8×C541 | C2 | semidirect |
| 22. C22⋊D541 | C8 | semidirect |
| 29. #16864513 | D4 | semidirect |
| 39. C22×C541 | C2×C8 | semidirect |
| 43. C2×D541 | C2×C8 | semidirect |
| 49. Dic541 | C2×C8 | semidirect |
| 55. C541 | C8×D4 | semidirect |
| 62. C22⋊C8 | D541 | semidirect |
| 98. C22 | C8×D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864513 | 2 |
| C2×C8×D541 | 2 |
| C4×C22⋊D541 | 2 |
| #31772557 | 2 |
| #31772540 | 2 |
| C8×Dic541 | 2 |
| C22⋊C8×C541 | 2 |
| C8×D4 | 541 |