Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1134 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 333 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. #22627074 | C2 | direct (N × H) |
| 21. C2×C4×Dic73 | C8 | semidirect |
| 22. C42×D73 | C8 | semidirect |
| 24. C2×C42×C73 | C8 | semidirect |
| 43. C4×Dic73 | C2×C8 | semidirect |
| 45. C42×C73 | C2×C8 | semidirect |
| 79. C2×C73 | #1839 | semidirect |
| 81. D73 | #1839 | semidirect |
| 87. C73 | C2×#1839 | semidirect |
| 108. C2×C42 | #10596842 | semidirect |
| 129. C42 | C2×#10596842 | semidirect |
| 165. C2 | #22627074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627074 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| C2×C42×#64408 | 2 |
| C2×#1839 | 73 |