Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 9. #17989500 | C4 | direct (N × H) |
| 15. C4×Dic292 | C4 | semidirect |
| 16. Q16×Dic73 | C4 | semidirect |
| 17. #17988681 | C4 | semidirect |
| 23. C4×Q16×C73 | C4 | semidirect |
| 76. Dic292 | C42 | semidirect |
| 96. Q16×C73 | C42 | semidirect |
| 143. C4×C73 | #358 | semidirect |
| 149. Dic73 | #358 | semidirect |
| 162. C73 | C4×#358 | semidirect |
| 171. C4×Q16 | #64408 | semidirect |
| 233. Q16 | C4×#64408 | semidirect |
| 305. C4 | #17989500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989500 | 2 |
| C4×#14556664 | 2 |
| C4×#14556660 | 2 |
| #22624988 | 2 |
| C4×Q16×D73 | 2 |
| C4×#358 | 73 |