Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22613090 | C2 | semidirect |
| 3. #22610768 | C2 | semidirect |
| 4. #22608448 | C2 | semidirect |
| 5. #22607836 | C2 | semidirect |
| 6. #22607783 | C2 | semidirect |
| 7. C73×#1510 | C2 | semidirect |
| 9. #17988905 | C4 | semidirect |
| 12. #17988721 | C4 | semidirect |
| 58. C22⋊#10596831 | C2×C4 | semidirect |
| 64. C22×D4×C73 | C2×C4 | semidirect |
| 71. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 252. #1510 | D73 | semidirect |
| 256. C73 | #9343 | semidirect |
| 283. C22×D4 | C4×D73 | semidirect |
| 300. C2×C4⋊C4 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620728 | 2 |
| #22613090 | 2 |
| #22610768 | 2 |
| #22608448 | 2 |
| #22607836 | 2 |
| #22607783 | 2 |
| C73×#1510 | 2 |
| #9343 | 73 |