Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
736 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 736 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. C2×#17989700 | C2 | semidirect |
| 2. #22627072 | C2 | semidirect |
| 4. #22626940 | 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 |
| 274. C73 | #9080 | 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 |
|---|---|
| C2×#17989700 | 2 |
| #22627072 | 2 |
| C2×#17989672 | 2 |
| #22626940 | 2 |
| C2×#17989537 | 2 |
| #9080 | 73 |