Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 82 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. #22625815 | C2 | semidirect |
| 3. #22625813 | C2 | semidirect |
| 4. #22625032 | C2 | semidirect |
| 15. C22×#11924011 | C4 | semidirect |
| 21. #17988614 | C4 | semidirect |
| 23. #17988550 | C4 | semidirect |
| 24. #405×C73 | C4 | semidirect |
| 191. C73 | #12806 | semidirect |
| 206. #405 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626184 | 2 |
| #22625815 | 2 |
| #22625813 | 2 |
| #22625032 | 2 |
| #22618636 | 2 |
| #12806 | 73 |