Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
12446 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 12446 conjugacy classes of subgroups — too many to draw. Only its 6264 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×Q8×#64408 | C2 | direct (N × H) |
| 7. C2×Q8×#64408 | C22 | direct (N × H) |
| 10. C23×Dic146 | C4 | semidirect |
| 11. C22×Q8×D73 | C4 | semidirect |
| 14. C23×Q8×C73 | C4 | semidirect |
| 16. C23×#64408 | Q8 | direct (N × H) |
| 19. Q8×#64408 | C23 | direct (N × H) |
| 23. C22×Dic146 | C2×C4 | semidirect |
| 24. C2×Q8×D73 | C2×C4 | semidirect |
| 29. C22×Q8×C73 | C2×C4 | semidirect |
| 32. C22×#64408 | C2×Q8 | direct (N × H) |
| 41. C2×Dic146 | C22×C4 | semidirect |
| 42. Q8×D73 | C22×C4 | semidirect |
| 48. C2×Q8×C73 | C22×C4 | semidirect |
| 50. C23×C73 | C4×Q8 | semidirect |
| 52. C22×D73 | C4×Q8 | semidirect |
| 58. C2×#64408 | C22×Q8 | direct (N × H) |
| 61. Q8×C73 | C23×C4 | semidirect |
| 66. Dic146 | C23×C4 | semidirect |
| 67. C22×C73 | C2×C4×Q8 | semidirect |
| 69. C2×D73 | C2×C4×Q8 | semidirect |
| 75. #64408 | C23×Q8 | direct (N × H) |
| 79. C2×C73 | C22×C4×Q8 | semidirect |
| 81. D73 | C22×C4×Q8 | semidirect |
| 88. C73 | C23×C4×Q8 | semidirect |
| 92. C23×Q8 | #64408 | direct (N × H) |
| 103. C22×Q8 | C2×#64408 | direct (N × H) |
| 123. C2×Q8 | C22×#64408 | direct (N × H) |
| 139. C23 | Q8×#64408 | direct (N × H) |
| 142. Q8 | C23×#64408 | direct (N × H) |
| 156. C22 | C2×Q8×#64408 | direct (N × H) |
| 165. C2 | C22×Q8×#64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×#64408 | 2 |
| C23×C4⋊#64408 | 2 |
| C23×C4×#64408 | 2 |
| C23×Q8×D73 | 2 |
| C23×C4×Q8 | 73 |