Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
984 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 213 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. #22627077 | C2 | semidirect |
| 2. #22627074 | C2 | semidirect |
| 23. #14556588 | C8 | semidirect |
| 24. #14556587 | C8 | semidirect |
| 26. #127×C73 | C8 | semidirect |
| 39. C2×D292 | C2×C8 | semidirect |
| 40. C2×C22⋊D73 | C2×C8 | semidirect |
| 44. C4×Dic73 | C2×C8 | semidirect |
| 45. C2×D4×C73 | C2×C8 | semidirect |
| 46. C42×C73 | C2×C8 | semidirect |
| 87. C73 | #23355 | semidirect |
| 102. #127 | #10596842 | semidirect |
| 116. C2×D4 | C2×#10596842 | semidirect |
| 130. C42 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627077 | 2 |
| #22627074 | 2 |
| #127×#64408 | 2 |
| #23355 | 73 |