Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #31771078 | C2 | semidirect |
| 3. C2×#22575367 | C2 | semidirect |
| 4. #31770460 | C2 | semidirect |
| 5. #31770460 | C2 | semidirect |
| 6. #31770371 | C2 | semidirect |
| 7. #342×C269 | C2 | semidirect |
| 12. #22575423 | C4 | semidirect |
| 33. C23×D269 | C2×C4 | semidirect |
| 45. C22×Dic269 | D4 | semidirect |
| 60. C22×C4×C269 | D4 | semidirect |
| 66. C22⋊C4×C269 | C2×C4 | semidirect |
| 87. C22×D269 | C22⋊C4 | semidirect |
| 99. C2×Dic269 | C22⋊C4 | semidirect |
| 160. C269 | #1889 | semidirect |
| 168. #342 | D269 | semidirect |
| 211. C22×C4 | D1076 | semidirect |
| 226. C22⋊C4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575423 | 2 |
| #31771078 | 2 |
| C2×#22575367 | 2 |
| #31770460 | 2 |
| #31770371 | 2 |
| #342×C269 | 2 |
| #1889 | 269 |