Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
254 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22608064 | C2 | direct (N × H) |
| 7. C2×#14556497 | C4 | semidirect |
| 12. C2×C32×C73 | C4 | semidirect |
| 20. #14556497 | C2×C4 | semidirect |
| 26. C32×C73 | C2×C4 | semidirect |
| 60. C2×C73 | #1397 | semidirect |
| 67. C73 | C2×#1397 | semidirect |
| 73. C2×C32 | Dic73 | semidirect |
| 89. C32 | C2×Dic73 | semidirect |
| 122. C2 | #22608064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556497 | 2 |
| C2×C16×Dic73 | 2 |
| #22608064 | 2 |
| C22×C32×C73 | 2 |
| C2×#1397 | 73 |