Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11927344 | C2 | semidirect |
| 2. C2×#10597354 | C2 | semidirect |
| 3. #11927113 | C2 | semidirect |
| 4. #11926560 | C2 | semidirect |
| 5. #11926550 | C2 | semidirect |
| 6. #11926517 | C2 | semidirect |
| 7. C19×#344 | C2 | semidirect |
| 51. C2×D76 | D4 | semidirect |
| 55. C2×Dic38 | D4 | semidirect |
| 59. M16×C19 | D4 | semidirect |
| 61. C2×C8×C19 | D4 | semidirect |
| 142. #344 | D19 | semidirect |
| 173. C19 | #2008 | semidirect |
| 208. M16 | D76 | semidirect |
| 210. C2×C8 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927344 | 2 |
| C2×#10597354 | 2 |
| #11927113 | 2 |
| #11926560 | 2 |
| #11926550 | 2 |
| #11926517 | 2 |
| C19×#344 | 2 |
| #2008 | 19 |