Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31771073 | C2 | semidirect |
| 3. #31770716 | C2 | semidirect |
| 4. #31770711 | C2 | semidirect |
| 5. #31770704 | C2 | semidirect |
| 6. #31770599 | C2 | semidirect |
| 7. C2×#22575363 | C2 | semidirect |
| 8. #427×C269 | C2 | semidirect |
| 10. #22575475 | C4 | semidirect |
| 30. #16864402 | C2×C4 | semidirect |
| 37. Dic1076 | C2×C4 | semidirect |
| 38. #16864391 | C2×C4 | semidirect |
| 39. D2152 | C2×C4 | semidirect |
| 48. C2×C8×C269 | C2×C4 | semidirect |
| 89. C269 | #2943 | semidirect |
| 96. #427 | D269 | semidirect |
| 133. C2×C8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| #31771073 | 2 |
| #31770716 | 2 |
| #31770711 | 2 |
| #31770704 | 2 |
| #31770599 | 2 |
| C2×#22575363 | 2 |
| #427×C269 | 2 |
| #2943 | 269 |