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. #23750332 | C2 | semidirect |
| 2. D4×Dic298 | C2 | semidirect |
| 3. #23750033 | C2 | semidirect |
| 4. #23750023 | C2 | semidirect |
| 5. #23749927 | C2 | semidirect |
| 6. #23749915 | C2 | semidirect |
| 7. #23749913 | C2 | semidirect |
| 8. #23749905 | C2 | semidirect |
| 9. #23749755 | C2 | semidirect |
| 65. D8×C149 | Q8 | semidirect |
| 89. D4×C149 | C2×Q8 | semidirect |
| 98. C8×C149 | C2×Q8 | semidirect |
| 121. C149 | #3384 | semidirect |
| 174. D8 | Dic298 | semidirect |
| 204. D4 | C2×Dic298 | semidirect |
| 220. C8 | C2×Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750332 | 2 |
| D4×Dic298 | 2 |
| #23750033 | 2 |
| #23750023 | 2 |
| #23749927 | 2 |
| #23749915 | 2 |
| #23749913 | 2 |
| #23749905 | 2 |
| #23749755 | 2 |
| #23749737 | 2 |
| C4×D8×C149 | 2 |
| #3384 | 149 |