Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#14558725 | C2 | semidirect |
| 2. C2×#18011890 | C2 | semidirect |
| 4. C2×#18011836 | C2 | semidirect |
| 5. C2×#18011833 | C2 | semidirect |
| 6. #23749388 | C2 | semidirect |
| 7. C2×C22⋊C8×C149 | C2 | semidirect |
| 35. C2×Dic298 | D4 | semidirect |
| 52. C4⋊Dic149 | D4 | semidirect |
| 70. C2×C8×C149 | D4 | semidirect |
| 102. C23×C149 | SD16 | semidirect |
| 157. C149 | #2000 | semidirect |
| 164. C2×C22⋊C8 | D149 | semidirect |
| 221. C2×C8 | C22⋊D149 | semidirect |
| 242. C23 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558725 | 2 |
| C2×#18011890 | 2 |
| C2×#18011885 | 2 |
| C2×#18011836 | 2 |
| C2×#18011833 | 2 |
| #23749388 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #2000 | 149 |