Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×D1076 | C2 | semidirect |
| 2. #31770951 | C2 | semidirect |
| 4. #31770352 | C2 | semidirect |
| 5. Q8⋊#14524130 | C2 | semidirect |
| 6. #31770332 | C2 | semidirect |
| 7. #460×C269 | C2 | semidirect |
| 56. D1076 | SD16 | semidirect |
| 66. Q8×C269 | D8 | semidirect |
| 99. C269 | #1627 | semidirect |
| 103. #460 | D269 | semidirect |
| 157. Q8 | #16864387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1076 | 2 |
| #31770951 | 2 |
| #31770797 | 2 |
| #31770352 | 2 |
| Q8⋊#14524130 | 2 |
| #31770332 | 2 |
| #460×C269 | 2 |
| #1627 | 269 |