Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 254 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 |
|---|---|---|
| 3. #22624957 | C2 | direct (N × H) |
| 24. C2×#11924003 | C8 | semidirect |
| 46. #11924003 | C2×C8 | semidirect |
| 83. C2×C73 | #1368 | semidirect |
| 91. C73 | C2×#1368 | semidirect |
| 169. C2 | #22624957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989448 | 2 |
| #22624957 | 2 |
| C2×#17988362 | 2 |
| C2×#1368 | 73 |