Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#22575825 | C2 | semidirect |
| 2. C2×#22575824 | C2 | semidirect |
| 3. C2×#22575821 | C2 | semidirect |
| 4. #31772624 | C2 | semidirect |
| 5. #31772615 | C2 | semidirect |
| 6. #31772538 | C2 | semidirect |
| 7. C2×D8×C541 | C2 | semidirect |
| 29. #16864513 | D4 | semidirect |
| 37. C8×C541 | D4 | semidirect |
| 54. C541 | #496 | semidirect |
| 59. C2×D8 | D541 | semidirect |
| 92. C8 | C22⋊D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575825 | 2 |
| C2×#22575824 | 2 |
| C2×#22575821 | 2 |
| #31772624 | 2 |
| #31772615 | 2 |
| #31772538 | 2 |
| C2×D8×C541 | 2 |
| #496 | 541 |