Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 203 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×#17988728 | C2 | semidirect |
| 3. C2×#17988507 | C2 | semidirect |
| 4. #22608902 | C2 | direct (N × H) |
| 5. C2×#17988322 | C2 | semidirect |
| 6. C2×#324×C73 | C2 | semidirect |
| 19. #17988728 | C22 | semidirect |
| 22. #17988507 | C22 | semidirect |
| 25. #17988322 | C22 | semidirect |
| 28. #324×C73 | C22 | semidirect |
| 130. C22×C4×C73 | SD16 | semidirect |
| 165. C2×C4×C73 | C2×SD16 | semidirect |
| 219. C2×C73 | #1604 | semidirect |
| 229. C2×#324 | D73 | semidirect |
| 230. C73 | C2×#1604 | semidirect |
| 252. #324 | C2×D73 | semidirect |
| 346. C22×C4 | #11924017 | semidirect |
| 412. C2×C4 | C2×#11924017 | semidirect |
| 443. C2 | #22608902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989168 | 2 |
| C2×#17988728 | 2 |
| C2×#17988507 | 2 |
| #22608902 | 2 |
| C2×#17988322 | 2 |
| C2×#324×C73 | 2 |
| C2×#1604 | 73 |