Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
556 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#17989676 | C2 | semidirect |
| 4. #22626937 | C2 | semidirect |
| 47. C22⋊#10596831 | C8 | semidirect |
| 48. #14556503 | C8 | semidirect |
| 49. C22⋊C8×C73 | C8 | semidirect |
| 90. C2×#10596831 | C2×C8 | semidirect |
| 94. C2×C8×C73 | C2×C8 | semidirect |
| 144. C22×C73 | #334 | semidirect |
| 152. C2×D73 | #334 | semidirect |
| 185. C73 | #8830 | semidirect |
| 227. C22⋊C8 | #10596842 | semidirect |
| 268. C2×C8 | C2×#10596842 | semidirect |
| 337. C22 | #17989676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10596842 | 2 |
| #22627071 | 2 |
| C2×#17989676 | 2 |
| #22626937 | 2 |
| C22⋊C8×#64408 | 2 |
| #8830 | 73 |