Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1134 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 2. #22610074 | C2 | semidirect |
| 3. #22610073 | C2 | semidirect |
| 5. C73×#1839 | C2 | semidirect |
| 31. C42×D73 | C8 | semidirect |
| 55. C4×Dic73 | C2×C8 | semidirect |
| 62. C42×C73 | C2×C8 | semidirect |
| 102. D73 | #1839 | direct (N × H) |
| 106. #1839 | D73 | direct (N × H) |
| 108. C73 | C2×#1839 | semidirect |
| 165. C42 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×D73 | 2 |
| #22610074 | 2 |
| #22610073 | 2 |
| #336×D73 | 2 |
| C73×#1839 | 2 |
| C2×#1839 | 73 |