Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #22608817 | C2 | semidirect |
| 3. #22608002 | C2 | semidirect |
| 4. #22607892 | C2 | semidirect |
| 5. #22607891 | C2 | semidirect |
| 6. C8×#11924003 | C2 | semidirect |
| 7. C73×#1589 | C2 | semidirect |
| 54. #11924003 | M16 | semidirect |
| 88. C8×C73 | D16 | semidirect |
| 114. #1589 | D73 | semidirect |
| 119. C73 | #12081 | semidirect |
| 201. C8 | #14556532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556532 | 2 |
| #22608817 | 2 |
| #22608002 | 2 |
| #22607892 | 2 |
| #22607891 | 2 |
| C8×#11924003 | 2 |
| C73×#1589 | 2 |
| #12081 | 73 |