Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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×#22575394 | C2 | semidirect |
| 2. #31770982 | C2 | semidirect |
| 3. C4⋊#16864377 | C2 | semidirect |
| 4. #31770405 | C2 | semidirect |
| 5. C4×D8×C269 | C2 | semidirect |
| 26. D8×C269 | D4 | semidirect |
| 57. C4×C269 | D16 | semidirect |
| 65. C269 | #2206 | semidirect |
| 69. C4×D8 | D269 | semidirect |
| 91. D8 | D1076 | semidirect |
| 123. C4 | #22575394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575394 | 2 |
| #31770982 | 2 |
| C4⋊#16864377 | 2 |
| #31770405 | 2 |
| C4×D8×C269 | 2 |
| #2206 | 269 |