Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
250 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #22627016 | C2 | semidirect |
| 3. C4×#14556681 | C2 | semidirect |
| 5. #17989695 | C4 | direct (N × H) |
| 14. #14556681 | C2×C4 | semidirect |
| 62. C4×C73 | M64 | semidirect |
| 73. C73 | C4×M64 | semidirect |
| 131. C4 | #17989695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989695 | 2 |
| #22627016 | 2 |
| C4×#14556681 | 2 |
| C2×C4×#11924031 | 2 |
| C4×M64 | 73 |