Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22611768 | C2 | semidirect |
| 3. #22611767 | C2 | semidirect |
| 4. #22608006 | C2 | semidirect |
| 5. #22607905 | C2 | semidirect |
| 6. C8×#11924003 | C2 | semidirect |
| 7. C73×#1335 | C2 | semidirect |
| 25. #14556537 | C8 | semidirect |
| 26. #14556535 | C8 | semidirect |
| 27. #14556534 | C8 | semidirect |
| 28. #14556532 | C8 | semidirect |
| 108. #1335 | D73 | semidirect |
| 110. C73 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611810 | 2 |
| #22611768 | 2 |
| #22611767 | 2 |
| #22608006 | 2 |
| #22607905 | 2 |
| C8×#11924003 | 2 |
| C73×#1335 | 2 |
| #12046 | 73 |