Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
722 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627173 | C2 | semidirect |
| 2. #22627051 | C2 | semidirect |
| 3. #22627045 | C2 | semidirect |
| 4. #22626936 | C2 | semidirect |
| 23. C4⋊#10596842 | D4 | semidirect |
| 50. #14556588 | C8 | semidirect |
| 52. #14556587 | C8 | semidirect |
| 53. #14556587 | C8 | semidirect |
| 55. #127×C73 | C8 | semidirect |
| 86. C2×D292 | C2×C8 | semidirect |
| 100. C4×Dic73 | C2×C8 | semidirect |
| 103. C2×D4×C73 | C2×C8 | semidirect |
| 104. C42×C73 | C2×C8 | semidirect |
| 198. C73 | #8959 | semidirect |
| 224. #127 | #10596842 | semidirect |
| 266. C2×D4 | C2×#10596842 | semidirect |
| 297. C42 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627173 | 2 |
| #22627051 | 2 |
| #22627045 | 2 |
| #22626936 | 2 |
| #127×#64408 | 2 |
| #8959 | 73 |