Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
246 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 3. #22624961 | C2 | semidirect |
| 4. #22624960 | C2 | semidirect |
| 5. #22624954 | C2 | semidirect |
| 6. #22624953 | C2 | semidirect |
| 53. #11924011 | C16 | semidirect |
| 87. C8×C73 | C2×C16 | semidirect |
| 91. #10596831 | C2×C16 | semidirect |
| 118. C73 | #12015 | semidirect |
| 204. C8 | #14556664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626291 | 2 |
| #22626261 | 2 |
| #22624961 | 2 |
| #22624960 | 2 |
| #22624954 | 2 |
| #22624953 | 2 |
| #22608210 | 2 |
| #12015 | 73 |