Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 3. #22626992 | C2 | semidirect |
| 4. #22626991 | C2 | semidirect |
| 35. #14556531 | C8 | semidirect |
| 36. #14556530 | C8 | semidirect |
| 38. M32×C73 | C8 | semidirect |
| 60. #11924003 | C2×C8 | semidirect |
| 62. C16×C73 | C2×C8 | semidirect |
| 109. C73 | #12000 | semidirect |
| 130. M32 | #10596842 | semidirect |
| 166. C16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| C2×#17989676 | 2 |
| #22626992 | 2 |
| #22626991 | 2 |
| M32×#64408 | 2 |
| #12000 | 73 |