Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1174 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 207 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. #22620853 | C2 | semidirect |
| 2. #22615136 | C2 | semidirect |
| 3. #22608900 | C2 | semidirect |
| 4. #22608426 | C2 | semidirect |
| 5. #22608255 | C2 | semidirect |
| 96. C2×Q8×C73 | SD16 | semidirect |
| 187. C73 | #18402 | semidirect |
| 267. C2×Q8 | #11924016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620853 | 2 |
| #22615136 | 2 |
| #22608900 | 2 |
| #22608426 | 2 |
| #22608255 | 2 |
| C73×#3497 | 2 |
| #18402 | 73 |