Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10597362 | C2 | semidirect |
| 2. #11927095 | C2 | semidirect |
| 3. C4×#64543 | C2 | semidirect |
| 4. #11926769 | C2 | semidirect |
| 5. #11926761 | C2 | semidirect |
| 6. #11926751 | C2 | semidirect |
| 7. #11926745 | C2 | semidirect |
| 8. #11926739 | C2 | semidirect |
| 9. C4⋊C8×D19 | C2 | semidirect |
| 10. #11926539 | C2 | semidirect |
| 11. C19×#461 | C2 | semidirect |
| 53. #64543 | D4 | semidirect |
| 137. C4×C19 | #135 | semidirect |
| 151. #461 | D19 | semidirect |
| 194. C19 | #3035 | semidirect |
| 292. C4 | #10597362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597362 | 2 |
| #11927095 | 2 |
| C4×#64543 | 2 |
| #11926769 | 2 |
| #11926761 | 2 |
| #11926751 | 2 |
| #11926745 | 2 |
| #11926739 | 2 |
| C4⋊C8×D19 | 2 |
| #11926539 | 2 |
| C19×#461 | 2 |
| #3035 | 19 |