Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 476 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 |
|---|---|---|
| 1. C2×#17989631 | C2 | semidirect |
| 2. C2×#17989502 | C2 | semidirect |
| 3. C2×#17989502 | C2 | semidirect |
| 4. #22626082 | C2 | semidirect |
| 5. #22624991 | C2 | semidirect |
| 6. #22624968 | C2 | semidirect |
| 24. C2×#14556534 | C4 | semidirect |
| 25. C2×#14556534 | C4 | semidirect |
| 26. C2×D1168 | C4 | semidirect |
| 28. C2×Q32×C73 | C4 | semidirect |
| 199. C73 | #13011 | semidirect |
| 205. C2×Q32 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989631 | 2 |
| C2×#17989502 | 2 |
| #22626082 | 2 |
| #22624991 | 2 |
| #22624968 | 2 |
| C2×#17989020 | 2 |
| #13011 | 73 |