Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
630 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22626934 | C2 | semidirect |
| 28. C4×#10596842 | D4 | semidirect |
| 49. #14556588 | C8 | semidirect |
| 51. #14556587 | C8 | semidirect |
| 52. #14556587 | C8 | semidirect |
| 54. #127×C73 | C8 | semidirect |
| 82. C2×D292 | C2×C8 | semidirect |
| 96. C4×Dic73 | C2×C8 | semidirect |
| 99. C2×D4×C73 | C2×C8 | semidirect |
| 100. C42×C73 | C2×C8 | semidirect |
| 193. C73 | #9101 | semidirect |
| 219. #127 | #10596842 | semidirect |
| 260. C2×D4 | C2×#10596842 | semidirect |
| 288. 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 |
| #22626934 | 2 |
| #22626423 | 2 |
| #9101 | 73 |