Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626321 | C2 | semidirect |
| 2. #22624958 | C2 | semidirect |
| 3. #22624895 | C2 | semidirect |
| 4. #22624847 | C2 | semidirect |
| 27. Q32×C73 | C8 | semidirect |
| 28. SD32×C73 | C8 | semidirect |
| 29. D16×C73 | C8 | semidirect |
| 73. C73 | #12068 | semidirect |
| 86. Q32 | #10596833 | semidirect |
| 87. SD32 | #10596833 | semidirect |
| 88. D16 | #10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626321 | 2 |
| #22624958 | 2 |
| #22624895 | 2 |
| #22624847 | 2 |
| #22611817 | 2 |
| #12068 | 73 |