Finite Group DatabasebetaFinite Group DatabasebetaOrder 1824.
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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. C3×Q8×D19 | C2 | semidirect |
| 3. #11744892 | C2 | semidirect |
| 4. C19×#216 | C2 | semidirect |
| 5. #11744827 | C2 | semidirect |
| 6. #11744824 | C2 | semidirect |
| 7. #11744815 | C2 | semidirect |
| 21. Q8×D19 | D3 | semidirect |
| 56. C3×C19 | #137 | semidirect |
| 60. #216 | D19 | semidirect |
| 79. C19 | #942 | semidirect |
| 115. C3 | #10597364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×D19 | 2 |
| #11744934 | 2 |
| #11744892 | 2 |
| C19×#216 | 2 |
| #11744827 | 2 |
| #11744824 | 2 |
| #11744815 | 2 |
| #10597364 | 3 |
| #942 | 19 |