Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
312 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. C2×#18011974 | C2 | semidirect |
| 4. D149⋊#101 | C2 | semidirect |
| 5. #23750504 | C2 | semidirect |
| 6. #23750500 | C2 | semidirect |
| 24. #18011944 | C4 | semidirect |
| 26. #18011942 | C4 | semidirect |
| 27. #18011941 | C4 | semidirect |
| 32. #137×C149 | C4 | semidirect |
| 147. C149 | #1908 | semidirect |
| 163. #137 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊#131 | 2 |
| #23750616 | 2 |
| C2×#18011974 | 2 |
| D149⋊#101 | 2 |
| #23750504 | 2 |
| #23750500 | 2 |
| #137×D149 | 2 |
| #1908 | 149 |