Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#22575377 | C2 | semidirect |
| 2. C2×#22575374 | C2 | semidirect |
| 3. C2×C22⋊#14524130 | C2 | semidirect |
| 4. #31770465 | C2 | semidirect |
| 16. C2×#41×C269 | C4 | semidirect |
| 70. Q8×C269 | C22⋊C4 | semidirect |
| 74. D4×C269 | C22⋊C4 | semidirect |
| 115. C269 | #1788 | semidirect |
| 125. C2×#41 | Dic269 | semidirect |
| 182. Q8 | C22⋊Dic269 | semidirect |
| 186. D4 | C22⋊Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575377 | 2 |
| C2×#22575374 | 2 |
| C2×C22⋊#14524130 | 2 |
| #31770465 | 2 |
| C22×#41×C269 | 2 |
| #1788 | 269 |