Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22612154 | C2 | semidirect |
| 2. #22612083 | C2 | semidirect |
| 3. #22609330 | C2 | semidirect |
| 4. #22607977 | C2 | semidirect |
| 5. #22607895 | C2 | semidirect |
| 6. D4⋊#11924003 | C2 | semidirect |
| 147. C73 | #12373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612154 | 2 |
| #22612083 | 2 |
| #22609330 | 2 |
| #22607977 | 2 |
| #22607895 | 2 |
| D4⋊#11924003 | 2 |
| C73×#3287 | 2 |
| #12373 | 73 |