Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597365 | C2 | semidirect |
| 2. #11927216 | C2 | semidirect |
| 3. #11927197 | C2 | semidirect |
| 4. #11926918 | C2 | semidirect |
| 5. #11926776 | C2 | semidirect |
| 6. #11926740 | C2 | semidirect |
| 7. #11926705 | C2 | semidirect |
| 8. #11926692 | C2 | semidirect |
| 9. C4×#64527 | C2 | semidirect |
| 10. #11926609 | C2 | semidirect |
| 11. C19×#462 | C2 | semidirect |
| 70. #64527 | D4 | semidirect |
| 130. C4×C19 | #135 | semidirect |
| 140. #462 | D19 | semidirect |
| 182. C19 | #3284 | semidirect |
| 272. C4 | #10597365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597365 | 2 |
| #11927216 | 2 |
| #11927197 | 2 |
| #11926918 | 2 |
| #11926776 | 2 |
| #11926740 | 2 |
| #11926705 | 2 |
| #11926692 | 2 |
| C4×#64527 | 2 |
| #11926609 | 2 |
| C19×#462 | 2 |
| #3284 | 19 |