Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 5. #17989682 | C4 | direct (N × H) |
| 6. C4×#11924040 | C4 | semidirect |
| 26. #11924040 | C42 | semidirect |
| 62. C4×C73 | #346 | semidirect |
| 64. Dic73 | #346 | semidirect |
| 74. C73 | C4×#346 | semidirect |
| 136. C4 | #17989682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989682 | 2 |
| C4×#14556686 | 2 |
| C4×C8×#64408 | 2 |
| C4×#346 | 73 |