Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 16. #22575363 | C4 | semidirect |
| 52. #14524130 | C4⋊C4 | semidirect |
| 64. C8×C269 | C4⋊C4 | semidirect |
| 84. C269 | #1847 | semidirect |
| 149. C8 | #16864381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575386 | 2 |
| C2×#22575385 | 2 |
| C2×#22575384 | 2 |
| C2×#22575363 | 2 |
| #31770474 | 2 |
| #31770470 | 2 |
| C2×#107×C269 | 2 |
| #1847 | 269 |