Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 96. C2×Dic146 | C2×C8 | semidirect |
| 109. C4⋊Dic73 | C2×C8 | semidirect |
| 116. C2×Q8×C73 | C2×C8 | semidirect |
| 119. C4⋊C4×C73 | C2×C8 | semidirect |
| 227. C73 | #7589 | semidirect |
| 259. C22⋊Q8 | #10596842 | semidirect |
| 288. C2×Q8 | C2×#10596842 | semidirect |
| 331. C4⋊C4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626932 | 2 |
| #22626931 | 2 |
| C22⋊Q8×#64408 | 2 |
| #7589 | 73 |