Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
662 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22627071 | C2 | semidirect |
| 2. C2×(C2×#10596842)⋊C4 | C2 | semidirect |
| 3. #22626931 | C2 | semidirect |
| 4. #22626930 | C2 | semidirect |
| 55. #14556566 | C8 | semidirect |
| 56. #14556565 | C8 | semidirect |
| 59. #14556562 | C8 | semidirect |
| 62. #121×C73 | C8 | semidirect |
| 105. C2×D292 | C2×C8 | semidirect |
| 121. C4⋊Dic73 | C2×C8 | semidirect |
| 127. C2×D4×C73 | C2×C8 | semidirect |
| 129. C4⋊C4×C73 | C2×C8 | semidirect |
| 256. C73 | #7586 | semidirect |
| 290. #121 | #10596842 | semidirect |
| 326. C2×D4 | C2×#10596842 | semidirect |
| 366. C4⋊C4 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627071 | 2 |
| C2×(C2×#10596842)⋊C4 | 2 |
| #22626931 | 2 |
| #22626930 | 2 |
| #121×#64408 | 2 |
| #7586 | 73 |