Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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. Q8×D57 | C2 | semidirect |
| 3. C19×#216 | C2 | semidirect |
| 4. C3×#64527 | C2 | semidirect |
| 5. #11744829 | C2 | semidirect |
| 6. #11744823 | C2 | semidirect |
| 7. #11744817 | C2 | semidirect |
| 24. #64527 | D3 | semidirect |
| 56. C3×C19 | #137 | semidirect |
| 60. #216 | D19 | semidirect |
| 79. C19 | #915 | semidirect |
| 115. C3 | #10597364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D57 | 2 |
| #11744927 | 2 |
| C19×#216 | 2 |
| C3×#64527 | 2 |
| #11744829 | 2 |
| #11744823 | 2 |
| #11744817 | 2 |
| #10597364 | 3 |
| #915 | 19 |