Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #31772716 | C2 | semidirect |
| 2. #31772715 | C2 | semidirect |
| 3. #31772699 | C2 | semidirect |
| 4. #31772693 | C2 | semidirect |
| 5. #31772692 | C2 | semidirect |
| 6. #31772682 | C2 | semidirect |
| 18. #22575826 | C4 | semidirect |
| 19. #22575825 | C4 | semidirect |
| 20. #22575821 | C4 | semidirect |
| 22. SD16×C541 | C4 | semidirect |
| 51. C541 | #444 | semidirect |
| 64. SD16 | #14524194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772716 | 2 |
| #31772715 | 2 |
| #31772699 | 2 |
| #31772693 | 2 |
| #31772692 | 2 |
| #31772682 | 2 |
| #31772649 | 2 |
| #444 | 541 |