Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
674 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 124 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. #22626778 | C2 | semidirect |
| 2. #22625167 | C2 | semidirect |
| 3. C2×#17989430 | C2 | semidirect |
| 4. #22624774 | C2 | semidirect |
| 33. C22⋊#10596833 | D4 | semidirect |
| 61. #120×C73 | C8 | semidirect |
| 104. C24×C73 | C2×C8 | semidirect |
| 117. C22⋊C4×C73 | C2×C8 | semidirect |
| 225. C73 | #9107 | semidirect |
| 255. #120 | #10596833 | semidirect |
| 291. C24 | C2×#10596833 | semidirect |
| 334. C22⋊C4 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626778 | 2 |
| #22625167 | 2 |
| C2×#17989430 | 2 |
| #22624774 | 2 |
| #22612592 | 2 |
| #9107 | 73 |