Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #31772676 | C2 | semidirect |
| 2. #31772675 | C2 | semidirect |
| 3. #31772661 | C2 | semidirect |
| 4. #31772660 | C2 | semidirect |
| 5. #31772657 | C2 | semidirect |
| 6. #31772649 | C2 | semidirect |
| 7. #31772648 | C2 | semidirect |
| 8. C2×#22575826 | C2 | semidirect |
| 9. Q16×D541 | C2 | semidirect |
| 10. #31772636 | C2 | semidirect |
| 11. #137×C541 | C2 | semidirect |
| 87. C541 | #578 | semidirect |
| 94. #137 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772676 | 2 |
| #31772675 | 2 |
| #31772661 | 2 |
| #31772660 | 2 |
| #31772657 | 2 |
| #31772649 | 2 |
| #31772648 | 2 |
| C2×#22575826 | 2 |
| Q16×D541 | 2 |
| #31772636 | 2 |
| #137×C541 | 2 |
| #578 | 541 |