Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597350 | C2 | semidirect |
| 2. #11927215 | C2 | semidirect |
| 3. #11927199 | C2 | semidirect |
| 4. #11926917 | C2 | semidirect |
| 5. #11926773 | C2 | semidirect |
| 6. #11926755 | C2 | semidirect |
| 7. #11926740 | C2 | semidirect |
| 8. #11926708 | C2 | semidirect |
| 9. #11926691 | C2 | semidirect |
| 10. C4×#64516 | C2 | semidirect |
| 11. C8×D4×C19 | C2 | semidirect |
| 81. #64516 | D4 | semidirect |
| 128. C4×C19 | #135 | semidirect |
| 145. C8×D4 | D19 | semidirect |
| 182. C19 | #3284 | semidirect |
| 272. C4 | #10597350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597350 | 2 |
| #11927215 | 2 |
| #11927199 | 2 |
| #11926917 | 2 |
| #11926773 | 2 |
| #11926755 | 2 |
| #11926740 | 2 |
| #11926708 | 2 |
| #11926691 | 2 |
| C4×#64516 | 2 |
| C8×D4×C19 | 2 |
| #3284 | 19 |