Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1354 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 254 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. Q8×C22⋊#64408 | C2 | semidirect |
| 2. #22626120 | C2 | semidirect |
| 17. C2×#14556589 | C4 | semidirect |
| 18. C2×#14556570 | C4 | semidirect |
| 20. C2×Q8×Dic73 | C4 | semidirect |
| 22. C23×Q8×C73 | C4 | semidirect |
| 29. #14556649 | Q8 | direct (N × H) |
| 66. C22⋊#64408 | C2×Q8 | semidirect |
| 110. C23×C73 | C4×Q8 | semidirect |
| 127. Q8×C73 | #99 | semidirect |
| 143. C2×Dic73 | C4×Q8 | semidirect |
| 187. C73 | Q8×#99 | semidirect |
| 189. C23×Q8 | #64408 | semidirect |
| 298. C23 | Q8×#64408 | semidirect |
| 305. Q8 | #14556649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊#64408 | 2 |
| #22626120 | 2 |
| #22625791 | 2 |
| C4×#14556649 | 2 |
| C2×Q8×C22⋊D73 | 2 |
| Q8×#99 | 73 |