Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
298 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22612158 | C2 | semidirect |
| 3. #22611978 | C2 | semidirect |
| 4. #22607990 | C2 | semidirect |
| 5. #22607894 | C2 | semidirect |
| 89. D4×C73 | Q32 | semidirect |
| 135. C73 | #12346 | semidirect |
| 220. D4 | #14556537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622324 | 2 |
| #22612158 | 2 |
| #22611978 | 2 |
| #22607990 | 2 |
| #22607894 | 2 |
| D4⋊#11924003 | 2 |
| C73×#1669 | 2 |
| #12346 | 73 |