Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1214 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 320 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. C2×#17989500 | C2 | direct (N × H) |
| 11. #17989500 | C22 | direct (N × H) |
| 13. C22×Dic292 | C4 | semidirect |
| 17. C2×Q16×D73 | C4 | semidirect |
| 20. C22×Q16×C73 | C4 | semidirect |
| 38. C2×Dic292 | C2×C4 | semidirect |
| 44. Q16×D73 | C2×C4 | semidirect |
| 53. C2×Q16×C73 | C2×C4 | semidirect |
| 79. Dic292 | C22×C4 | semidirect |
| 94. Q16×C73 | C22×C4 | semidirect |
| 127. C22×C73 | #358 | semidirect |
| 129. C2×D73 | #358 | semidirect |
| 142. C2×C73 | C2×#358 | semidirect |
| 144. D73 | C2×#358 | semidirect |
| 151. C73 | C22×#358 | semidirect |
| 159. C22×Q16 | #64408 | semidirect |
| 188. C2×Q16 | C2×#64408 | semidirect |
| 231. Q16 | C22×#64408 | semidirect |
| 279. C22 | #17989500 | direct (N × H) |
| 291. C2 | C2×#17989500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556664 | 2 |
| C22×#14556660 | 2 |
| C2×#17989500 | 2 |
| C22×Q16×D73 | 2 |
| C22×#358 | 73 |