Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 221 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. C8×#11924040 | C2 | semidirect |
| 12. #14556686 | C8 | direct (N × H) |
| 26. #11924040 | C2×C8 | semidirect |
| 27. #11924036 | C16 | semidirect |
| 36. C8×D73 | C16 | semidirect |
| 53. #10596833 | C2×C16 | semidirect |
| 55. C8×C73 | C2×C16 | semidirect |
| 56. #10596831 | C2×C16 | semidirect |
| 71. D73 | C8×C16 | semidirect |
| 75. C73 | C2×C8×C16 | semidirect |
| 128. C8 | #14556686 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556686 | 2 |
| C8×#11924040 | 2 |
| C8×#11924036 | 2 |
| C2×C8×C16 | 73 |