Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
250 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22627018 | C2 | semidirect |
| 3. #64408⋊C32 | C2 | semidirect |
| 5. #17989696 | C4 | semidirect |
| 6. #17989695 | C4 | semidirect |
| 15. #14556681 | C2×C4 | semidirect |
| 75. #64408 | M64 | semidirect |
| 89. C73 | C4×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627162 | 2 |
| #22627018 | 2 |
| #64408⋊C32 | 2 |
| C2×C16×#64408 | 2 |
| C4×M64 | 73 |