Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#18011844 | C2 | semidirect |
| 5. #23749524 | C2 | semidirect |
| 6. #23749379 | C2 | semidirect |
| 7. #340×C149 | C2 | semidirect |
| 19. #18011831 | C4 | semidirect |
| 39. C2×#11924746 | C2×C4 | semidirect |
| 54. C4⋊C4×C149 | C2×C4 | semidirect |
| 66. D596 | C4⋊C4 | semidirect |
| 123. C149 | #1862 | semidirect |
| 130. #340 | D149 | semidirect |
| 175. C4⋊C4 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011873 | 2 |
| C2×#18011844 | 2 |
| C2×#18011833 | 2 |
| C2×#18011831 | 2 |
| #23749524 | 2 |
| #23749379 | 2 |
| #340×C149 | 2 |
| #1862 | 149 |