Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. #23750653 | C2 | semidirect |
| 2. D4×#11924753 | C2 | semidirect |
| 3. #23750489 | C2 | semidirect |
| 4. #23750473 | C2 | semidirect |
| 5. D4⋊#11924753 | C2 | semidirect |
| 6. C8×#11924753 | C2 | semidirect |
| 33. #14558721 | C8 | semidirect |
| 46. #11924753 | D8 | semidirect |
| 49. D596 | C2×C8 | semidirect |
| 57. #11924746 | C2×C8 | semidirect |
| 60. D4×C149 | C2×C8 | semidirect |
| 83. C149 | C8×D8 | semidirect |
| 131. D4 | D149⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750653 | 2 |
| D4×#11924753 | 2 |
| #23750489 | 2 |
| #23750473 | 2 |
| D4⋊#11924753 | 2 |
| C8×#11924753 | 2 |
| #23749705 | 2 |
| C8×D8 | 149 |