Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
600 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 115 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. C4×C4⋊#10596842 | C2 | semidirect |
| 2. C4×C4⋊#10596842 | C2 | semidirect |
| 3. C2×Q8⋊#10596842 | C2 | semidirect |
| 57. #14556580 | C8 | semidirect |
| 58. #14556579 | C8 | semidirect |
| 59. #14556578 | C8 | semidirect |
| 65. #124×C73 | C8 | semidirect |
| 229. C73 | #9675 | semidirect |
| 259. #124 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| C2×Q8⋊#10596842 | 2 |
| C2×D4⋊#10596842 | 2 |
| #124×#64408 | 2 |
| #9675 | 73 |