Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
726 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 147 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. #22607861 | C2 | direct (N × H) |
| 25. C23×C4×C73 | C8 | semidirect |
| 71. C22×C4×C73 | C2×C8 | semidirect |
| 155. C2×C73 | #1317 | semidirect |
| 161. C73 | C2×#1317 | semidirect |
| 180. C23×C4 | #10596831 | semidirect |
| 227. C22×C4 | C2×#10596831 | semidirect |
| 312. C2 | #22607861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988311 | 2 |
| #22607861 | 2 |
| C2×#381×C73 | 2 |
| C2×#1317 | 73 |