Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 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. #23750676 | C2 | semidirect |
| 2. #23750658 | C2 | semidirect |
| 3. #23750656 | C2 | semidirect |
| 4. #23750654 | C2 | semidirect |
| 5. #23750649 | C2 | semidirect |
| 6. #23750647 | C2 | semidirect |
| 7. #23750631 | C2 | semidirect |
| 8. #23750630 | C2 | semidirect |
| 114. C149 | #2995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750676 | 2 |
| #23750658 | 2 |
| #23750656 | 2 |
| #23750654 | 2 |
| #23750649 | 2 |
| #23750647 | 2 |
| #23750631 | 2 |
| #23750630 | 2 |
| #23750154 | 2 |
| #2995 | 149 |