Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. D4×Dic298 | C2 | semidirect |
| 2. #23750290 | C2 | semidirect |
| 3. #23750029 | C2 | semidirect |
| 4. #23750028 | C2 | semidirect |
| 5. #23749906 | C2 | semidirect |
| 6. #23749904 | C2 | semidirect |
| 7. #23749903 | C2 | semidirect |
| 8. #23749749 | C2 | semidirect |
| 11. #474×C149 | C2 | semidirect |
| 51. #14558721 | Q8 | semidirect |
| 78. Dic298 | D8 | semidirect |
| 80. D596 | C2×Q8 | semidirect |
| 89. #11924746 | C2×Q8 | semidirect |
| 93. D4×C149 | C2×Q8 | semidirect |
| 123. C149 | Q8×D8 | semidirect |
| 132. #474 | D149 | semidirect |
| 208. D4 | Q8×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic298 | 2 |
| #23750290 | 2 |
| #23750029 | 2 |
| #23750028 | 2 |
| #23749906 | 2 |
| #23749904 | 2 |
| #23749903 | 2 |
| #23749749 | 2 |
| C4×#14558721 | 2 |
| #23749705 | 2 |
| #474×C149 | 2 |
| Q8×D8 | 149 |