Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1470 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 320 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. C22×#14556664 | C2 | semidirect |
| 2. C22×#14556660 | C2 | semidirect |
| 3. C2×#17989499 | C2 | direct (N × H) |
| 7. C2×#14556664 | C22 | semidirect |
| 10. C2×#14556660 | C22 | semidirect |
| 11. #17989499 | C22 | direct (N × H) |
| 13. C22×D584 | C4 | semidirect |
| 17. C2×D8×D73 | C4 | semidirect |
| 20. C22×D8×C73 | C4 | semidirect |
| 25. #14556664 | C23 | semidirect |
| 28. #14556660 | C23 | semidirect |
| 38. C2×D584 | C2×C4 | semidirect |
| 44. D8×D73 | C2×C4 | semidirect |
| 53. C2×D8×C73 | C2×C4 | semidirect |
| 81. D584 | C22×C4 | semidirect |
| 96. D8×C73 | C22×C4 | semidirect |
| 136. C22×C73 | #357 | semidirect |
| 143. C2×D73 | #357 | semidirect |
| 155. C2×C73 | C2×#357 | semidirect |
| 158. D73 | C2×#357 | semidirect |
| 165. C73 | C22×#357 | semidirect |
| 173. C22×D8 | #64408 | semidirect |
| 202. C2×D8 | C2×#64408 | semidirect |
| 247. D8 | C22×#64408 | semidirect |
| 307. C22 | #17989499 | direct (N × H) |
| 319. C2 | C2×#17989499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556664 | 2 |
| C22×#14556660 | 2 |
| C2×#17989499 | 2 |
| C22×D8×D73 | 2 |
| C22×#357 | 73 |