Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
| 3. #23749976 | C2 | semidirect |
| 4. #23749956 | C2 | semidirect |
| 5. #23749911 | C2 | semidirect |
| 6. #23749854 | C2 | semidirect |
| 7. #23749831 | C2 | semidirect |
| 8. #23749766 | C2 | semidirect |
| 9. C4×#14558725 | C2 | semidirect |
| 10. C2×#18011836 | C2 | semidirect |
| 11. C8×D4×C149 | C2 | semidirect |
| 83. Dic298 | #41 | semidirect |
| 96. D4×C149 | SD16 | semidirect |
| 128. C149 | #3298 | semidirect |
| 139. C8×D4 | D149 | semidirect |
| 217. D4 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic298 | 2 |
| #23750279 | 2 |
| #23749976 | 2 |
| #23749956 | 2 |
| #23749911 | 2 |
| #23749854 | 2 |
| #23749831 | 2 |
| #23749766 | 2 |
| C4×#14558725 | 2 |
| C2×#18011836 | 2 |
| C8×D4×C149 | 2 |
| #3298 | 149 |