Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. #22627186 | C2 | semidirect |
| 2. #22627115 | C2 | semidirect |
| 3. #22627109 | C2 | semidirect |
| 4. #22627005 | C2 | semidirect |
| 23. #14556688 | D4 | semidirect |
| 148. C73 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627186 | 2 |
| #22627115 | 2 |
| #22627109 | 2 |
| #22627005 | 2 |
| #22626656 | 2 |
| #12982 | 73 |