Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23750099 | C2 | semidirect |
| 3. #23749643 | C2 | semidirect |
| 4. #23749629 | C2 | semidirect |
| 5. #23749598 | C2 | semidirect |
| 6. #23749396 | C2 | semidirect |
| 7. H(3,ℤ/4)×C149 | C2 | semidirect |
| 12. C2×#14558725 | C4 | semidirect |
| 13. C2×D1192 | C4 | semidirect |
| 30. C2×Dic298 | C2×C4 | semidirect |
| 35. C2×D596 | C2×C4 | semidirect |
| 53. C2×C8×C149 | C2×C4 | semidirect |
| 115. C149 | #1904 | semidirect |
| 123. H(3,ℤ/4) | D149 | semidirect |
| 165. C2×C8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011939 | 2 |
| #23750099 | 2 |
| #23749643 | 2 |
| #23749629 | 2 |
| #23749598 | 2 |
| #23749396 | 2 |
| H(3,ℤ/4)×C149 | 2 |
| #1904 | 149 |