Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
226 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22608827 | C2 | semidirect |
| 4. #22607894 | C2 | semidirect |
| 6. #22607850 | C2 | semidirect |
| 7. C73×#1371 | C2 | semidirect |
| 109. #1371 | D73 | semidirect |
| 113. C73 | #12074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556536 | 2 |
| #22608827 | 2 |
| #22608725 | 2 |
| #22607894 | 2 |
| #22607891 | 2 |
| #22607850 | 2 |
| C73×#1371 | 2 |
| #12074 | 73 |