Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22617893 | C2 | semidirect |
| 5. #22607756 | C2 | semidirect |
| 6. #22607756 | C2 | semidirect |
| 7. C73×#1271 | C2 | semidirect |
| 73. C2×Dic146 | SD16 | semidirect |
| 123. C4⋊C4×C73 | SD16 | semidirect |
| 223. #1271 | D73 | semidirect |
| 224. C73 | #7748 | semidirect |
| 339. C4⋊C4 | #11924017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617893 | 2 |
| #22611165 | 2 |
| #22611021 | 2 |
| #22607756 | 2 |
| C73×#1271 | 2 |
| #7748 | 73 |