Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
596 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #22626932 | C2 | semidirect |
| 4. #22626931 | C2 | semidirect |
| 52. #14556571 | C8 | semidirect |
| 53. #14556570 | C8 | semidirect |
| 56. #14556567 | C8 | semidirect |
| 60. C22⋊Q8×C73 | C8 | semidirect |
| 94. C2×Dic146 | C2×C8 | semidirect |
| 107. C4⋊Dic73 | C2×C8 | semidirect |
| 114. C2×Q8×C73 | C2×C8 | semidirect |
| 117. C4⋊C4×C73 | C2×C8 | semidirect |
| 222. C73 | #7566 | semidirect |
| 254. C22⋊Q8 | #10596842 | semidirect |
| 283. C2×Q8 | C2×#10596842 | semidirect |
| 324. C4⋊C4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#10596842 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626932 | 2 |
| #22626931 | 2 |
| C22⋊Q8×#64408 | 2 |
| #7566 | 73 |