Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×#14556664 | C2 | semidirect |
| 2. #22625481 | C2 | semidirect |
| 3. #22624887 | C2 | semidirect |
| 4. #22624886 | C2 | semidirect |
| 30. #14556614 | C8 | semidirect |
| 153. C73 | #11591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556664 | 2 |
| #22625481 | 2 |
| #22624887 | 2 |
| #22624886 | 2 |
| C4×#14556614 | 2 |
| #11591 | 73 |