Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #23750354 | C2 | semidirect |
| 3. #23750032 | C2 | semidirect |
| 4. #23750030 | C2 | semidirect |
| 6. #23749918 | C2 | semidirect |
| 7. #23749910 | C2 | semidirect |
| 9. #23749755 | C2 | semidirect |
| 64. SD16×C149 | Q8 | semidirect |
| 85. Q8×C149 | C2×Q8 | semidirect |
| 96. C8×C149 | C2×Q8 | semidirect |
| 116. C149 | #3386 | semidirect |
| 167. SD16 | Dic298 | semidirect |
| 196. Q8 | C2×Dic298 | semidirect |
| 213. C8 | C2×Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750354 | 2 |
| D4×Dic298 | 2 |
| #23750032 | 2 |
| #23750030 | 2 |
| #23749923 | 2 |
| #23749918 | 2 |
| #23749910 | 2 |
| #23749905 | 2 |
| #23749755 | 2 |
| #23749726 | 2 |
| C4×SD16×C149 | 2 |
| #3386 | 149 |