Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23750347 | C2 | semidirect |
| 2. #23750018 | C2 | semidirect |
| 4. #23749847 | C2 | semidirect |
| 6. #23749834 | C2 | semidirect |
| 7. #23749755 | C2 | semidirect |
| 8. #23749724 | C2 | semidirect |
| 9. C4×Q16×C149 | C2 | semidirect |
| 102. C149 | #3402 | semidirect |
| 112. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750347 | 2 |
| #23750018 | 2 |
| #23750009 | 2 |
| #23749847 | 2 |
| #23749843 | 2 |
| #23749834 | 2 |
| #23749755 | 2 |
| #23749724 | 2 |
| C4×Q16×C149 | 2 |
| #3402 | 149 |