Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750354 | C2 | semidirect |
| 3. #23750032 | C2 | semidirect |
| 4. #23750028 | C2 | semidirect |
| 6. #23749918 | C2 | semidirect |
| 8. #23749752 | C2 | semidirect |
| 11. #475×C149 | C2 | semidirect |
| 48. #14558723 | Q8 | semidirect |
| 86. #11924746 | C2×Q8 | semidirect |
| 89. Q8×C149 | C2×Q8 | semidirect |
| 116. C149 | #3386 | semidirect |
| 124. #475 | D149 | semidirect |
| 196. Q8 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750354 | 2 |
| #23750290 | 2 |
| #23750032 | 2 |
| #23750028 | 2 |
| #23749924 | 2 |
| #23749918 | 2 |
| #23749906 | 2 |
| #23749752 | 2 |
| #23749728 | 2 |
| C4×#14558723 | 2 |
| #475×C149 | 2 |
| #3386 | 149 |