Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750029 | C2 | semidirect |
| 3. #23750003 | C2 | semidirect |
| 4. #23749974 | C2 | semidirect |
| 8. C4×Dic596 | C2 | semidirect |
| 9. C4×#14558726 | C2 | semidirect |
| 11. C4×Q16×C149 | C2 | semidirect |
| 83. C4×D149 | Q16 | semidirect |
| 114. C149 | #3170 | semidirect |
| 125. C4×Q16 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750179 | 2 |
| #23750029 | 2 |
| #23750003 | 2 |
| #23749974 | 2 |
| #23749867 | 2 |
| #23749865 | 2 |
| #23749863 | 2 |
| C4×Dic596 | 2 |
| C4×#14558726 | 2 |
| C4×C8×D149 | 2 |
| C4×Q16×C149 | 2 |
| #3170 | 149 |