Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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. #31771230 | C2 | semidirect |
| 2. #31770758 | C2 | semidirect |
| 3. #31770755 | C2 | semidirect |
| 5. #31770341 | C2 | semidirect |
| 6. #31770328 | C2 | semidirect |
| 7. #328×C269 | C2 | semidirect |
| 30. C2×Dic538 | D4 | semidirect |
| 44. C4⋊Dic269 | D4 | semidirect |
| 54. C2×Q8×C269 | D4 | semidirect |
| 59. C4⋊C4×C269 | D4 | semidirect |
| 72. C22×D269 | SD16 | semidirect |
| 130. C269 | #1596 | semidirect |
| 137. #328 | D269 | semidirect |
| 162. C2×Q8 | D1076 | semidirect |
| 184. C4⋊C4 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771230 | 2 |
| #31770758 | 2 |
| #31770755 | 2 |
| #31770515 | 2 |
| #31770341 | 2 |
| #31770328 | 2 |
| #328×C269 | 2 |
| #1596 | 269 |