Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
438 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. C2×#17989477 | C2 | semidirect |
| 4. #22625746 | C2 | semidirect |
| 5. #22625005 | C2 | semidirect |
| 6. #22624996 | C2 | semidirect |
| 11. #17989633 | C4 | semidirect |
| 17. #17989504 | C4 | semidirect |
| 23. #17988391 | C4 | semidirect |
| 24. #17988389 | C4 | semidirect |
| 25. #17988387 | C4 | semidirect |
| 26. #358×C73 | C4 | semidirect |
| 92. D584 | C42 | semidirect |
| 103. Q16×C73 | C42 | semidirect |
| 171. C73 | #12650 | semidirect |
| 186. #358 | #64408 | semidirect |
| 241. Q16 | C4×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989633 | 2 |
| C2×#17989504 | 2 |
| C2×#17989477 | 2 |
| #22625746 | 2 |
| #22625005 | 2 |
| #22624996 | 2 |
| #22611642 | 2 |
| #12650 | 73 |