Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
790 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 18. #17988344 | C4 | semidirect |
| 19. #17988343 | C4 | semidirect |
| 20. H(3,ℤ/4)×C73 | C4 | semidirect |
| 89. C2×#10596831 | C4⋊C4 | semidirect |
| 97. C4×Dic73 | C4⋊C4 | semidirect |
| 100. C2×C8×C73 | C4⋊C4 | semidirect |
| 103. C42×C73 | C4⋊C4 | semidirect |
| 173. C73 | #11335 | semidirect |
| 187. H(3,ℤ/4) | #64408 | semidirect |
| 252. C2×C8 | C4⋊#64408 | semidirect |
| 271. C42 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626584 | 2 |
| #22626391 | 2 |
| #22625612 | 2 |
| #22625593 | 2 |
| H(3,ℤ/4)×D73 | 2 |
| #11335 | 73 |