Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23749972 | C2 | semidirect |
| 3. #23749906 | C2 | semidirect |
| 4. #23749835 | C2 | semidirect |
| 5. #23749368 | C2 | semidirect |
| 6. #23749354 | C2 | semidirect |
| 7. Q8⋊C8×C149 | C2 | semidirect |
| 99. C149 | #1641 | semidirect |
| 106. Q8⋊C8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750297 | 2 |
| #23749972 | 2 |
| #23749906 | 2 |
| #23749835 | 2 |
| #23749368 | 2 |
| #23749354 | 2 |
| Q8⋊C8×C149 | 2 |
| #1641 | 149 |