Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
444 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 10. C4×Dic538 | C4 | semidirect |
| 85. C269 | #2320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic538 | 2 |
| #31770510 | 2 |
| #31770501 | 2 |
| #31770489 | 2 |
| #31770472 | 2 |
| #31770469 | 2 |
| #31770451 | 2 |
| C4×C4⋊C4×C269 | 2 |
| #2320 | 269 |