Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22608755 | C2 | semidirect |
| 2. #22607997 | C2 | semidirect |
| 3. #22607898 | C2 | semidirect |
| 4. #22607851 | C2 | semidirect |
| 23. D16×C73 | C8 | semidirect |
| 36. D8×C73 | C2×C8 | semidirect |
| 43. C16×C73 | C2×C8 | semidirect |
| 74. C73 | #12067 | semidirect |
| 88. D16 | #10596831 | semidirect |
| 101. D8 | C2×#10596831 | semidirect |
| 112. C16 | C2×#10596831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22608755 | 2 |
| #22607997 | 2 |
| #22607898 | 2 |
| #22607851 | 2 |
| C73×#2177 | 2 |
| #12067 | 73 |