Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 2. C2×#22575823 | C2 | semidirect |
| 3. #31772635 | C2 | semidirect |
| 4. #31772563 | C2 | semidirect |
| 5. #31772547 | C2 | semidirect |
| 6. #31772544 | C2 | semidirect |
| 7. #137×C541 | C2 | semidirect |
| 51. C541 | #471 | semidirect |
| 53. #137 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772653 | 2 |
| C2×#22575823 | 2 |
| #31772635 | 2 |
| #31772563 | 2 |
| #31772547 | 2 |
| #31772544 | 2 |
| #137×C541 | 2 |
| #471 | 541 |