Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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. #23749532 | C2 | semidirect |
| 3. #23749517 | C2 | semidirect |
| 4. #23749515 | C2 | semidirect |
| 6. C4×#14558713 | C2 | semidirect |
| 7. #23749472 | C2 | semidirect |
| 8. #23749470 | C2 | semidirect |
| 9. #391×C149 | C2 | semidirect |
| 12. #18011900 | C4 | semidirect |
| 46. #14558713 | C2×C4 | semidirect |
| 47. #14558713 | C2×C4 | semidirect |
| 51. C4×Dic149 | C2×C4 | semidirect |
| 54. C2×Q8×C149 | C2×C4 | semidirect |
| 123. C149 | #2372 | semidirect |
| 127. #391 | D149 | semidirect |
| 159. C2×Q8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011900 | 2 |
| #23749532 | 2 |
| #23749517 | 2 |
| #23749515 | 2 |
| #23749503 | 2 |
| C4×#14558713 | 2 |
| #23749472 | 2 |
| #23749470 | 2 |
| #391×C149 | 2 |
| #2372 | 149 |