Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
602 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 127 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. #22618972 | C2 | semidirect |
| 2. #22608322 | C2 | semidirect |
| 3. #22608252 | C2 | semidirect |
| 4. #22607760 | C2 | semidirect |
| 28. C4×#10596831 | D4 | semidirect |
| 67. C2×D4×C73 | M16 | semidirect |
| 89. C42×C73 | M16 | semidirect |
| 169. C73 | #9105 | semidirect |
| 228. C2×D4 | #11924012 | semidirect |
| 253. C42 | #11924012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618972 | 2 |
| #22608322 | 2 |
| #22608252 | 2 |
| #22607760 | 2 |
| C73×#2328 | 2 |
| #9105 | 73 |