Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
496 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626241 | C2 | semidirect |
| 4. #22626093 | C2 | semidirect |
| 5. #22624993 | C2 | semidirect |
| 6. #22624984 | C2 | semidirect |
| 22. C2×#14556536 | C4 | semidirect |
| 23. C2×#14556535 | C4 | semidirect |
| 24. C2×#14556534 | C4 | semidirect |
| 28. C2×SD32×C73 | C4 | semidirect |
| 50. C2×Dic292 | C2×C4 | semidirect |
| 66. C2×#11924003 | C2×C4 | semidirect |
| 69. C2×Q16×C73 | C2×C4 | semidirect |
| 72. C2×C16×C73 | C2×C4 | semidirect |
| 194. C73 | #13019 | semidirect |
| 203. C2×SD32 | #64408 | semidirect |
| 224. C2×Q16 | C2×#64408 | semidirect |
| 250. C2×C16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626690 | 2 |
| D73⋊#361 | 2 |
| #22626241 | 2 |
| #22626093 | 2 |
| #22624993 | 2 |
| #22624984 | 2 |
| C2×SD32×D73 | 2 |
| #13019 | 73 |