Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
626 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 172 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. #22624771 | C2 | semidirect |
| 55. C2×#10596831 | M16 | semidirect |
| 76. C2×C8×C73 | M16 | semidirect |
| 126. C73 | #7919 | semidirect |
| 189. C2×C8 | #11924037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626607 | 2 |
| #22624771 | 2 |
| C22×#14556501 | 2 |
| #7919 | 73 |