Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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×Dic292 | C2 | semidirect |
| 4. #22608005 | C2 | semidirect |
| 5. #22607896 | C2 | semidirect |
| 7. C8×C16×C73 | C2 | semidirect |
| 28. #14556536 | C8 | direct (N × H) |
| 48. Dic292 | C2×C8 | semidirect |
| 67. C16×C73 | C2×C8 | semidirect |
| 84. C8×C73 | SD32 | semidirect |
| 112. C8×C16 | D73 | semidirect |
| 113. C73 | C8×SD32 | semidirect |
| 173. C16 | C8×D73 | semidirect |
| 192. C8 | #14556536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556536 | 2 |
| C8×Dic292 | 2 |
| C8×D584 | 2 |
| #22608005 | 2 |
| #22607896 | 2 |
| #22607893 | 2 |
| C8×C16×C73 | 2 |
| C8×SD32 | 73 |