Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2190 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 2190 conjugacy classes of subgroups — too many to draw. Only its 1063 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. #22627175 | C2 | semidirect |
| 2. #22627174 | C2 | semidirect |
| 3. #41×#10596842 | C2 | semidirect |
| 4. C2×Q8×#10596842 | C2 | semidirect |
| 34. #14556639 | C8 | semidirect |
| 35. #14556638 | C8 | semidirect |
| 38. 2−1+4×C73 | C8 | semidirect |
| 51. #11924029 | C2×C8 | semidirect |
| 52. #11924028 | C2×C8 | semidirect |
| 53. #11924027 | C2×C8 | semidirect |
| 54. C2×Dic146 | C2×C8 | semidirect |
| 55. Q8×D73 | C2×C8 | semidirect |
| 59. #41×C73 | C2×C8 | semidirect |
| 60. C2×Q8×C73 | C2×C8 | semidirect |
| 70. #10596842 | 2−1+4 | direct (N × H) |
| 102. C73 | C8×2−1+4 | semidirect |
| 118. 2−1+4 | #10596842 | direct (N × H) |
| 139. #41 | C2×#10596842 | semidirect |
| 143. C2×Q8 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627175 | 2 |
| #22627174 | 2 |
| #41×#10596842 | 2 |
| C2×Q8×#10596842 | 2 |
| 2−1+4×#64408 | 2 |
| C8×2−1+4 | 73 |