Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1486 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1486 conjugacy classes of subgroups — too many to draw. Only its 272 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. #22625119 | C2 | semidirect |
| 3. #22625117 | C2 | semidirect |
| 16. #17988450 | C4 | semidirect |
| 17. #17988449 | C4 | semidirect |
| 18. #17988448 | C4 | semidirect |
| 20. #381×C73 | C4 | semidirect |
| 74. C22×Dic73 | C4⋊C4 | semidirect |
| 87. C2×C4×D73 | C4⋊C4 | semidirect |
| 94. C22×C4×C73 | C4⋊C4 | semidirect |
| 189. C73 | #14674 | semidirect |
| 199. #381 | #64408 | semidirect |
| 272. C22×C4 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989529 | 2 |
| #22625119 | 2 |
| #22625117 | 2 |
| #22625114 | 2 |
| #381×D73 | 2 |
| #14674 | 73 |