Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
204 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #22611773 | C2 | semidirect |
| 2. #22607999 | C2 | semidirect |
| 3. #22607907 | C2 | semidirect |
| 4. #22607851 | C2 | semidirect |
| 23. Q32×C73 | C8 | semidirect |
| 24. SD32×C73 | C8 | semidirect |
| 25. D16×C73 | C8 | semidirect |
| 73. C73 | #12068 | semidirect |
| 86. Q32 | #10596831 | semidirect |
| 87. SD32 | #10596831 | semidirect |
| 88. D16 | #10596831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611773 | 2 |
| #22607999 | 2 |
| #22607907 | 2 |
| #22607851 | 2 |
| C73×#2179 | 2 |
| #12068 | 73 |