Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
534 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 534 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×#10597322 | C2 | semidirect |
| 2. C2×#10597321 | C2 | semidirect |
| 3. #11926466 | C2 | semidirect |
| 4. #11926465 | C2 | semidirect |
| 5. #11926462 | C2 | semidirect |
| 6. #11926461 | C2 | semidirect |
| 7. #11926457 | C2 | semidirect |
| 9. #11926446 | C2 | semidirect |
| 10. #11926435 | C2 | semidirect |
| 11. C4×C4⋊C4×C19 | C2 | semidirect |
| 57. C42×C19 | D4 | semidirect |
| 147. C4×C4⋊C4 | D19 | semidirect |
| 180. C19 | #2662 | semidirect |
| 214. C42 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597322 | 2 |
| C2×#10597321 | 2 |
| #11926466 | 2 |
| #11926465 | 2 |
| #11926462 | 2 |
| #11926461 | 2 |
| #11926457 | 2 |
| #11926454 | 2 |
| #11926446 | 2 |
| #11926435 | 2 |
| C4×C4⋊C4×C19 | 2 |
| #2662 | 19 |