Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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. #22624750 | C2 | semidirect |
| 4. #22624749 | C2 | semidirect |
| 34. #14556549 | C8 | semidirect |
| 83. C4⋊Dic73 | C2×C8 | semidirect |
| 102. C4⋊C4×C73 | C2×C8 | semidirect |
| 191. C73 | #7579 | semidirect |
| 281. C4⋊C4 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625823 | 2 |
| #22625592 | 2 |
| #22624750 | 2 |
| #22624749 | 2 |
| #22612412 | 2 |
| #7579 | 73 |