Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
606 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626121 | C2 | semidirect |
| 4. C2×#17989440 | C2 | semidirect |
| 5. #22624806 | C2 | semidirect |
| 6. #22624772 | C2 | semidirect |
| 27. #17988905 | C4 | semidirect |
| 31. #17988728 | C4 | semidirect |
| 32. #17988725 | C4 | semidirect |
| 34. #481×C73 | C4 | semidirect |
| 59. C22×Dic146 | C2×C4 | semidirect |
| 83. C22⋊#10596831 | C2×C4 | semidirect |
| 86. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 89. C22⋊C8×C73 | C2×C4 | semidirect |
| 114. C22⋊#64408 | SD16 | semidirect |
| 291. C73 | #9275 | semidirect |
| 297. #481 | #64408 | semidirect |
| 345. C2×C4⋊C4 | C2×#64408 | semidirect |
| 366. C22⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626459 | 2 |
| #22626121 | 2 |
| #22625366 | 2 |
| C2×#17989440 | 2 |
| #22624806 | 2 |
| #22624772 | 2 |
| #22620690 | 2 |
| #9275 | 73 |