Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. C22×#14556497 | C2 | semidirect |
| 3. #22608108 | C2 | direct (N × H) |
| 4. C2×#366×C73 | C2 | semidirect |
| 8. C2×D1168 | C4 | semidirect |
| 11. C2×#14556497 | C22 | semidirect |
| 15. #366×C73 | C22 | semidirect |
| 23. D1168 | C2×C4 | semidirect |
| 82. C2×C73 | #1415 | semidirect |
| 89. C2×#366 | D73 | semidirect |
| 91. C73 | C2×#1415 | semidirect |
| 102. #366 | C2×D73 | semidirect |
| 169. C2 | #22608108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1168 | 2 |
| C22×#14556497 | 2 |
| #22608108 | 2 |
| C2×#366×C73 | 2 |
| C2×#1415 | 73 |