Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
526 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22610972 | C2 | semidirect |
| 2. #22608933 | C2 | semidirect |
| 3. #22608865 | C2 | semidirect |
| 4. #22607937 | C2 | semidirect |
| 5. #22607934 | C2 | semidirect |
| 6. #22607863 | C2 | semidirect |
| 7. C73×#2699 | C2 | semidirect |
| 102. C2×D4×C73 | D8 | semidirect |
| 223. #2699 | D73 | semidirect |
| 230. C73 | #12099 | semidirect |
| 312. C2×D4 | #11924013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610972 | 2 |
| #22608933 | 2 |
| #22608865 | 2 |
| #22607937 | 2 |
| #22607934 | 2 |
| #22607863 | 2 |
| C73×#2699 | 2 |
| #12099 | 73 |