Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
340 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 3. #22625079 | C2 | semidirect |
| 4. #22625078 | C2 | semidirect |
| 5. #22625077 | C2 | semidirect |
| 6. #22625076 | C2 | semidirect |
| 16. #125×D73 | C4 | semidirect |
| 21. #17988941 | C4 | semidirect |
| 25. C4×C8×D73 | C4 | semidirect |
| 26. #488×C73 | C4 | semidirect |
| 38. #14556583 | C2×C4 | semidirect |
| 55. C4×#10596831 | C2×C4 | semidirect |
| 57. #125×C73 | C2×C4 | semidirect |
| 61. C4×C8×C73 | C2×C4 | semidirect |
| 162. D73 | #1414 | semidirect |
| 170. C73 | C2×#1414 | semidirect |
| 178. #488 | #64408 | semidirect |
| 197. #125 | C2×#64408 | semidirect |
| 224. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#355 | 2 |
| D73⋊#354 | 2 |
| #22625079 | 2 |
| #22625078 | 2 |
| #22625077 | 2 |
| #22625076 | 2 |
| #488×D73 | 2 |
| C2×#1414 | 73 |