Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22610921 | C2 | semidirect |
| 3. #22608690 | C2 | semidirect |
| 4. #22608612 | C2 | semidirect |
| 6. #22608220 | C2 | semidirect |
| 127. C8×C73 | #100 | semidirect |
| 161. C73 | #9805 | semidirect |
| 285. C8 | #14556508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610921 | 2 |
| #22610772 | 2 |
| #22608690 | 2 |
| #22608612 | 2 |
| #22608599 | 2 |
| #22608220 | 2 |
| C2×#492×C73 | 2 |
| #9805 | 73 |