Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
720 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22627071 | C2 | semidirect |
| 2. C4×C22⋊#10596842 | C2 | semidirect |
| 3. C2×#17989673 | C2 | semidirect |
| 60. C2×C22⋊Dic73 | C8 | semidirect |
| 61. C2×#11924005 | C8 | semidirect |
| 62. C2×#11924005 | C8 | semidirect |
| 67. C2×C22⋊C4×C73 | C8 | semidirect |
| 273. C73 | #9651 | semidirect |
| 320. C2×C22⋊C4 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C4×C22⋊#10596842 | 2 |
| C2×#17989673 | 2 |
| C2×#17989672 | 2 |
| C2×#17989537 | 2 |
| #9651 | 73 |