Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22623034 | C2 | semidirect |
| 3. #22611558 | C2 | semidirect |
| 4. #22608012 | C2 | semidirect |
| 5. C73×#2115 | C2 | semidirect |
| 37. #14556531 | D4 | semidirect |
| 146. #2115 | D73 | semidirect |
| 148. C73 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623034 | 2 |
| #22618641 | 2 |
| #22611558 | 2 |
| #22608012 | 2 |
| C73×#2115 | 2 |
| #12982 | 73 |