Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 16. #18011822 | C4 | semidirect |
| 17. C4×#11924746 | C4 | semidirect |
| 78. C149 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011846 | 2 |
| #23749661 | 2 |
| #23749581 | 2 |
| #23749397 | 2 |
| #23749395 | 2 |
| #23749381 | 2 |
| H(3,ℤ/4)×C149 | 2 |
| #1833 | 149 |