Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #23750589 | C2 | semidirect |
| 4. #23750506 | C2 | semidirect |
| 8. C2×#14558746 | C4 | semidirect |
| 9. C2×#14558745 | C4 | semidirect |
| 12. C2×D149⋊C8 | C4 | semidirect |
| 13. C22×#11924753 | C4 | semidirect |
| 15. #18011972 | C4 | semidirect |
| 16. #18011971 | C4 | semidirect |
| 97. C149 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011998 | 2 |
| #23750612 | 2 |
| #23750589 | 2 |
| #23750506 | 2 |
| #23749597 | 2 |
| #1757 | 149 |