Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
534 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| 3. #22625339 | C2 | semidirect |
| 5. #22624833 | C2 | semidirect |
| 6. #22624780 | C2 | semidirect |
| 27. #17988900 | C4 | semidirect |
| 31. #17988728 | C4 | semidirect |
| 32. #17988725 | C4 | semidirect |
| 34. #480×C73 | C4 | semidirect |
| 57. C22×Dic146 | C2×C4 | semidirect |
| 81. C22⋊#10596831 | C2×C4 | semidirect |
| 84. C2×C4⋊C4×C73 | C2×C4 | semidirect |
| 87. C22⋊C8×C73 | C2×C4 | semidirect |
| 268. C73 | #9341 | semidirect |
| 273. #480 | #64408 | semidirect |
| 319. C2×C4⋊C4 | C2×#64408 | semidirect |
| 341. C22⋊C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626472 | 2 |
| #22626121 | 2 |
| #22625339 | 2 |
| #22625326 | 2 |
| #22624833 | 2 |
| #22624780 | 2 |
| #22620739 | 2 |
| #9341 | 73 |