Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #22608005 | C2 | semidirect |
| 5. #22608004 | C2 | semidirect |
| 6. #22608002 | C2 | semidirect |
| 7. C73×#1371 | C2 | semidirect |
| 59. #11924003 | M16 | semidirect |
| 66. C16×C73 | M16 | semidirect |
| 111. #1371 | D73 | semidirect |
| 112. C73 | #12025 | semidirect |
| 171. C16 | #11924011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556530 | 2 |
| #22608693 | 2 |
| #22608688 | 2 |
| #22608005 | 2 |
| #22608004 | 2 |
| #22608002 | 2 |
| C73×#1371 | 2 |
| #12025 | 73 |