Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 15. #18011843 | C4 | semidirect |
| 16. #18011842 | C4 | semidirect |
| 17. #106×C149 | C4 | semidirect |
| 55. #11924746 | C4⋊C4 | semidirect |
| 58. C8×C149 | C4⋊C4 | semidirect |
| 78. C149 | #1944 | semidirect |
| 94. #106 | #10597010 | semidirect |
| 137. C8 | C4⋊#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011980 | 2 |
| C2×#18011965 | 2 |
| #23750576 | 2 |
| #23750498 | 2 |
| #106×D149 | 2 |
| #1944 | 149 |