Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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×#18011980 | C2 | semidirect |
| 3. C2×#18011979 | C2 | semidirect |
| 5. #23750499 | C2 | semidirect |
| 6. #23750499 | C2 | semidirect |
| 23. C22⋊#11924746 | C4 | semidirect |
| 24. #18011823 | C4 | semidirect |
| 25. #18011823 | C4 | semidirect |
| 26. C22⋊C8×C149 | C4 | semidirect |
| 140. C149 | #1854 | semidirect |
| 166. C22⋊C8 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011990 | 2 |
| C2×#18011980 | 2 |
| C2×#18011979 | 2 |
| #23750567 | 2 |
| #23750499 | 2 |
| C22⋊C8×D149 | 2 |
| #1854 | 149 |