Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
356 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 146 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. #23750677 | C2 | semidirect |
| 2. #23750655 | C2 | semidirect |
| 3. #23750655 | C2 | semidirect |
| 4. #23750653 | C2 | semidirect |
| 5. #23750650 | C2 | semidirect |
| 6. #23750648 | C2 | semidirect |
| 7. #23750632 | C2 | semidirect |
| 8. D149⋊(C4⋊C8) | C2 | semidirect |
| 114. C149 | #2992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750677 | 2 |
| #23750655 | 2 |
| #23750653 | 2 |
| #23750650 | 2 |
| #23750648 | 2 |
| #23750632 | 2 |
| D149⋊(C4⋊C8) | 2 |
| #23750160 | 2 |
| #2992 | 149 |