Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1214 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 280 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×#14556666 | C2 | semidirect |
| 2. C22×#14556659 | C2 | semidirect |
| 3. C2×#17989504 | C2 | direct (N × H) |
| 7. C2×#14556666 | C22 | semidirect |
| 10. C2×#14556659 | C22 | semidirect |
| 11. #17989504 | C22 | direct (N × H) |
| 15. C2×#14556614 | C4 | semidirect |
| 18. C22×D584 | C4 | semidirect |
| 20. C22×Q16×C73 | C4 | semidirect |
| 25. #14556666 | C23 | semidirect |
| 28. #14556659 | C23 | semidirect |
| 40. #14556614 | C2×C4 | semidirect |
| 45. C2×D584 | C2×C4 | semidirect |
| 53. C2×Q16×C73 | C2×C4 | semidirect |
| 81. D584 | C22×C4 | semidirect |
| 94. Q16×C73 | C22×C4 | semidirect |
| 127. C22×C73 | #360 | semidirect |
| 142. C2×C73 | C2×#360 | semidirect |
| 151. C73 | C22×#360 | semidirect |
| 157. C22×Q16 | #64408 | semidirect |
| 184. C2×Q16 | C2×#64408 | semidirect |
| 227. Q16 | C22×#64408 | semidirect |
| 280. C22 | #17989504 | direct (N × H) |
| 291. C2 | C2×#17989504 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556666 | 2 |
| C22×#14556659 | 2 |
| C2×#17989504 | 2 |
| C22×#14556614 | 2 |
| C22×#360 | 73 |