Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
614 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22⋊C4×#10596842 | C2 | semidirect |
| 4. #22626942 | C2 | semidirect |
| 6. C23×#10596842 | C4 | semidirect |
| 10. C2×C4⋊#10596842 | C4 | semidirect |
| 11. C2×C22⋊#10596842 | C4 | semidirect |
| 15. C2×C4×#10596842 | C4 | semidirect |
| 17. #17989673 | C4 | semidirect |
| 18. #17989672 | C4 | semidirect |
| 53. #14556650 | C8 | semidirect |
| 54. #14556649 | C8 | semidirect |
| 58. #14556506 | C8 | semidirect |
| 59. #14556505 | C8 | semidirect |
| 60. #99×C73 | C8 | semidirect |
| 94. C22⋊#64408 | C2×C8 | semidirect |
| 108. C22⋊Dic73 | C2×C8 | semidirect |
| 111. C22⋊C4×C73 | C2×C8 | semidirect |
| 112. C23×C73 | C4×C8 | semidirect |
| 120. C22×D73 | C4×C8 | semidirect |
| 149. #10596842 | #99 | direct (N × H) |
| 152. C2×C4×C73 | C4×C8 | semidirect |
| 156. C2×Dic73 | C4×C8 | semidirect |
| 207. C73 | C8×#99 | semidirect |
| 254. #99 | #10596842 | direct (N × H) |
| 309. C22⋊C4 | C2×#10596842 | semidirect |
| 325. C23 | C4×#10596842 | semidirect |
| 357. C2×C4 | C4×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10596842 | 2 |
| C22⋊C4×#10596842 | 2 |
| #22627044 | 2 |
| #22626942 | 2 |
| #99×#64408 | 2 |
| C8×#99 | 73 |