Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22626931 | C2 | semidirect |
| 4. #22626931 | C2 | semidirect |
| 50. #14556550 | C8 | semidirect |
| 51. #14556549 | C8 | semidirect |
| 52. #14556549 | C8 | semidirect |
| 59. #117×C73 | C8 | semidirect |
| 103. C4⋊Dic73 | C2×C8 | semidirect |
| 104. C4⋊Dic73 | C2×C8 | semidirect |
| 114. C4⋊C4×C73 | C2×C8 | semidirect |
| 115. C4⋊C4×C73 | C2×C8 | semidirect |
| 218. C73 | #7579 | semidirect |
| 250. #117 | #10596842 | semidirect |
| 315. C4⋊C4 | C2×#10596842 | semidirect |
| 316. C4⋊C4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627072 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626931 | 2 |
| #22626391 | 2 |
| #7579 | 73 |