Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. #22624846 | C2 | semidirect |
| 4. #22624846 | C2 | semidirect |
| 5. #22624843 | C2 | semidirect |
| 6. C8×#11924031 | C2 | semidirect |
| 46. #11924031 | M16 | semidirect |
| 81. #10596831 | M32 | semidirect |
| 107. C73 | #11409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626290 | 2 |
| C4×#14556666 | 2 |
| #22624846 | 2 |
| #22624843 | 2 |
| C8×#11924031 | 2 |
| #22608210 | 2 |
| #11409 | 73 |