Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
726 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 128 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. #22624857 | C2 | direct (N × H) |
| 36. C23×C4×C73 | C8 | semidirect |
| 77. C22×C4×C73 | C2×C8 | semidirect |
| 155. C2×C73 | #1317 | semidirect |
| 161. C73 | C2×#1317 | semidirect |
| 181. C23×C4 | #10596833 | semidirect |
| 228. C22×C4 | C2×#10596833 | semidirect |
| 312. C2 | #22624857 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989430 | 2 |
| #22624857 | 2 |
| C2×#17988450 | 2 |
| C2×#1317 | 73 |