Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1080 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 234 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. #22626054 | C2 | semidirect |
| 2. #22626001 | C2 | semidirect |
| 3. #22625905 | C2 | semidirect |
| 4. #22625753 | C2 | semidirect |
| 6. C22×#11924036 | C22 | semidirect |
| 7. C2×#14556658 | C22 | semidirect |
| 8. C2×#14556648 | C22 | semidirect |
| 11. C2×C4×#10596833 | C22 | semidirect |
| 12. #17989453 | C22 | semidirect |
| 34. #14556560 | C8 | semidirect |
| 68. C22⋊Dic73 | C2×C8 | semidirect |
| 74. C24×C73 | C2×C8 | semidirect |
| 140. C73 | #23306 | semidirect |
| 183. C24 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626054 | 2 |
| #22626001 | 2 |
| #22625905 | 2 |
| #22625753 | 2 |
| #22612430 | 2 |
| #23306 | 73 |