Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#18011821 | C2 | semidirect |
| 5. C4⋊C4×Dic149 | C2 | semidirect |
| 6. #23749387 | C2 | semidirect |
| 7. #340×C149 | C2 | semidirect |
| 12. #18011873 | C4 | semidirect |
| 17. #18011833 | C4 | semidirect |
| 18. #18011831 | C4 | semidirect |
| 39. C2×#11924746 | C2×C4 | semidirect |
| 41. C4⋊Dic149 | C2×C4 | semidirect |
| 51. C2×C8×C149 | C2×C4 | semidirect |
| 55. C4⋊C4×C149 | C2×C4 | semidirect |
| 66. D596 | C42 | semidirect |
| 123. C149 | #1762 | semidirect |
| 131. #340 | D149 | semidirect |
| 169. C2×C8 | C4×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×#18011833 | 2 |
| C2×#18011831 | 2 |
| C2×#18011821 | 2 |
| C4⋊C4×Dic149 | 2 |
| #23749387 | 2 |
| #340×C149 | 2 |
| #1762 | 149 |