Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
998 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 108 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×#14556651 | C2 | semidirect |
| 2. #22625392 | C2 | semidirect |
| 3. #22625273 | C2 | semidirect |
| 4. #22625190 | C2 | semidirect |
| 162. Q8×C73 | #100 | semidirect |
| 238. C73 | #8369 | semidirect |
| 395. Q8 | #14556651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556651 | 2 |
| #22625392 | 2 |
| #22625273 | 2 |
| #22625190 | 2 |
| C2×#17989248 | 2 |
| #8369 | 73 |