Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
690 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 106 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. #22626110 | C2 | semidirect |
| 3. #22626097 | C2 | semidirect |
| 5. #22624766 | C2 | semidirect |
| 6. #22624766 | C2 | semidirect |
| 24. #17988935 | C4 | semidirect |
| 25. #17988934 | C4 | semidirect |
| 26. #17988933 | C4 | semidirect |
| 30. #486×C73 | C4 | semidirect |
| 60. #14556591 | C2×C4 | semidirect |
| 74. C4×#10596831 | C2×C4 | semidirect |
| 76. C4⋊Q8×C73 | C2×C4 | semidirect |
| 79. C4×C8×C73 | C2×C4 | semidirect |
| 270. C73 | #9057 | semidirect |
| 279. #486 | #64408 | semidirect |
| 306. C4⋊Q8 | C2×#64408 | semidirect |
| 340. C4×C8 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626461 | 2 |
| #22626110 | 2 |
| #22626097 | 2 |
| D73⋊#331 | 2 |
| #22624766 | 2 |
| #486×D73 | 2 |
| #9057 | 73 |