Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#64408⋊C16 | C2 | semidirect |
| 2. #22627055 | C2 | semidirect |
| 3. #22626978 | C2 | semidirect |
| 4. #22626977 | C2 | semidirect |
| 52. #14556614 | C8 | semidirect |
| 53. #14556613 | C8 | semidirect |
| 56. #14556610 | C8 | semidirect |
| 61. #135×C73 | C8 | semidirect |
| 187. C73 | #11591 | semidirect |
| 211. #135 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64408⋊C16 | 2 |
| #22627055 | 2 |
| #22626978 | 2 |
| #22626977 | 2 |
| #135×#64408 | 2 |
| #11591 | 73 |