Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
558 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22627076 | C2 | semidirect |
| 4. #22626942 | C2 | semidirect |
| 54. #14556506 | C8 | semidirect |
| 55. #14556505 | C8 | semidirect |
| 56. #99×C73 | C8 | semidirect |
| 102. C22⋊Dic73 | C2×C8 | semidirect |
| 105. C22⋊C4×C73 | C2×C8 | semidirect |
| 106. C23×C73 | C4⋊C8 | semidirect |
| 114. C22×D73 | C4⋊C8 | semidirect |
| 144. C2×C4×C73 | C4⋊C8 | semidirect |
| 148. C2×Dic73 | C4⋊C8 | semidirect |
| 199. C73 | #8851 | semidirect |
| 243. #99 | #10596842 | semidirect |
| 295. C22⋊C4 | C2×#10596842 | semidirect |
| 311. C23 | C4⋊#10596842 | semidirect |
| 343. C2×C4 | C4⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627173 | 2 |
| #22627077 | 2 |
| #22627076 | 2 |
| #22626942 | 2 |
| #99×#64408 | 2 |
| #8851 | 73 |