Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #23750353 | C2 | semidirect |
| 3. #23750027 | C2 | semidirect |
| 4. #23750023 | C2 | semidirect |
| 5. #23749933 | C2 | semidirect |
| 7. #23749921 | C2 | semidirect |
| 11. C8×Q8×C149 | C2 | semidirect |
| 47. #14558725 | Q8 | semidirect |
| 114. C149 | #3381 | semidirect |
| 124. C8×Q8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750353 | 2 |
| #23750335 | 2 |
| #23750027 | 2 |
| #23750023 | 2 |
| #23749933 | 2 |
| #23749926 | 2 |
| #23749921 | 2 |
| #23749906 | 2 |
| C4×#14558725 | 2 |
| C8×Q8×C149 | 2 |
| #3381 | 149 |