Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #31771321 | C2 | direct (N × H) |
| 2. C2×#22575442 | C2 | semidirect |
| 3. C2×#22575428 | C2 | semidirect |
| 4. C2×C4×D1076 | C2 | semidirect |
| 5. C2×#22575411 | C2 | semidirect |
| 6. C2×C4⋊Q8×C269 | C2 | semidirect |
| 10. #22575442 | C22 | semidirect |
| 11. #22575428 | C22 | semidirect |
| 12. C4×D1076 | C22 | semidirect |
| 13. #22575411 | C22 | semidirect |
| 19. C4⋊Q8×C269 | C22 | semidirect |
| 69. C2×C269 | #555 | semidirect |
| 73. C269 | C2×#555 | semidirect |
| 76. C2×C4⋊Q8 | D269 | semidirect |
| 85. C4⋊Q8 | C2×D269 | semidirect |
| 144. C2 | #31771321 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771321 | 2 |
| C2×#22575442 | 2 |
| C2×#22575428 | 2 |
| C2×C4×D1076 | 2 |
| C2×#22575411 | 2 |
| C2×C4⋊Q8×C269 | 2 |
| C2×#555 | 269 |