Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 3. #22625325 | C2 | semidirect |
| 4. #22625323 | C2 | semidirect |
| 5. #22624820 | C2 | semidirect |
| 6. #22624820 | C2 | semidirect |
| 26. #17988949 | C4 | semidirect |
| 27. #17988947 | C4 | semidirect |
| 28. #17988946 | C4 | semidirect |
| 34. #489×C73 | C4 | semidirect |
| 60. #14556591 | C2×C4 | semidirect |
| 81. #14556502 | C2×C4 | semidirect |
| 83. C4⋊Q8×C73 | C2×C4 | semidirect |
| 87. #97×C73 | C2×C4 | semidirect |
| 239. C73 | #9439 | semidirect |
| 245. #489 | #64408 | semidirect |
| 272. C4⋊Q8 | C2×#64408 | semidirect |
| 310. #97 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626467 | 2 |
| #22625411 | 2 |
| #22625325 | 2 |
| #22625323 | 2 |
| #22624820 | 2 |
| #22620316 | 2 |
| #9439 | 73 |