Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22627080 | C2 | semidirect |
| 4. C2×#17989671 | C2 | semidirect |
| 5. #22626939 | C2 | semidirect |
| 6. #22626937 | C2 | semidirect |
| 59. #14556513 | C8 | semidirect |
| 60. #14556512 | C8 | semidirect |
| 61. #14556511 | C8 | semidirect |
| 62. #102×C73 | C8 | semidirect |
| 221. C73 | #9556 | semidirect |
| 267. #102 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627081 | 2 |
| #22627080 | 2 |
| C2×D4⋊#10596842 | 2 |
| C2×#17989671 | 2 |
| #22626939 | 2 |
| #22626937 | 2 |
| #102×#64408 | 2 |
| #9556 | 73 |