Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1470 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 549 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. #22627075 | C2 | direct (N × H) |
| 24. C2×C4×Dic73 | C8 | semidirect |
| 25. C42×D73 | C8 | semidirect |
| 27. C2×C42×C73 | C8 | semidirect |
| 47. C4×Dic73 | C2×C8 | semidirect |
| 49. C42×C73 | C2×C8 | semidirect |
| 64. C2×C4×C73 | C4⋊C8 | semidirect |
| 66. C2×Dic73 | C4⋊C8 | semidirect |
| 68. C4×D73 | C4⋊C8 | semidirect |
| 82. C4×C73 | C2×C4⋊C8 | semidirect |
| 83. Dic73 | C2×C4⋊C8 | semidirect |
| 85. C2×C73 | #1842 | semidirect |
| 87. D73 | #1842 | semidirect |
| 93. C73 | C2×#1842 | semidirect |
| 116. C2×C42 | #10596842 | semidirect |
| 139. C42 | C2×#10596842 | semidirect |
| 158. C2×C4 | C4⋊#10596842 | semidirect |
| 173. C4 | C2×C4⋊#10596842 | semidirect |
| 177. C2 | #22627075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10596842 | 2 |
| #22627075 | 2 |
| C2×C42×#64408 | 2 |
| C2×#1842 | 73 |