Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
658 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22625881 | C2 | semidirect |
| 4. #22625117 | C2 | semidirect |
| 5. #22624805 | C2 | semidirect |
| 6. #22624768 | C2 | semidirect |
| 27. #17988322 | C4 | semidirect |
| 28. #17988321 | C4 | semidirect |
| 29. #17988320 | C4 | semidirect |
| 30. #327×C73 | C4 | semidirect |
| 72. C22⋊#10596831 | C2×C4 | semidirect |
| 75. #14556498 | C2×C4 | semidirect |
| 77. C22⋊C8×C73 | C2×C4 | semidirect |
| 78. #95×C73 | C2×C4 | semidirect |
| 310. C73 | #8870 | semidirect |
| 333. #327 | #64408 | semidirect |
| 371. C22⋊C8 | C2×#64408 | semidirect |
| 381. #95 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626420 | 2 |
| #22625918 | 2 |
| #22625881 | 2 |
| #22625117 | 2 |
| #22624805 | 2 |
| #22624768 | 2 |
| #327×D73 | 2 |
| #8870 | 73 |