Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#17989506 | C2 | semidirect |
| 4. #22626079 | C2 | semidirect |
| 5. #22624996 | C2 | semidirect |
| 6. #22624971 | C2 | semidirect |
| 24. C2×#14556537 | C4 | semidirect |
| 25. C2×#14556536 | C4 | semidirect |
| 26. C2×#14556534 | C4 | semidirect |
| 28. C2×Q32×C73 | C4 | semidirect |
| 196. C73 | #13039 | semidirect |
| 203. C2×Q32 | #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×#17989506 | 2 |
| C2×#17989504 | 2 |
| #22626079 | 2 |
| #22624996 | 2 |
| #22624971 | 2 |
| C2×#17989029 | 2 |
| #13039 | 73 |