Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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×D596 | C2 | semidirect |
| 2. #23750035 | C2 | semidirect |
| 3. #23750021 | C2 | semidirect |
| 4. #23749922 | C2 | semidirect |
| 5. #23749915 | C2 | semidirect |
| 6. #23749912 | C2 | semidirect |
| 7. #23749905 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 11. #554×C149 | C2 | semidirect |
| 47. #14558721 | Q8 | semidirect |
| 84. #11924746 | C2×Q8 | semidirect |
| 89. D4×C149 | C2×Q8 | semidirect |
| 121. C149 | #3384 | semidirect |
| 123. #554 | D149 | semidirect |
| 204. D4 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D596 | 2 |
| #23750035 | 2 |
| #23750021 | 2 |
| #23749922 | 2 |
| #23749915 | 2 |
| #23749912 | 2 |
| #23749905 | 2 |
| #23749756 | 2 |
| #23749735 | 2 |
| C4×#14558721 | 2 |
| #554×C149 | 2 |
| #3384 | 149 |