Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×#17989514 | C2 | semidirect |
| 4. #22626035 | C2 | semidirect |
| 5. #22624988 | C2 | semidirect |
| 6. #22624968 | C2 | semidirect |
| 23. #17988389 | C4 | semidirect |
| 24. #17988388 | C4 | semidirect |
| 25. #17988387 | C4 | semidirect |
| 26. #357×C73 | C4 | semidirect |
| 56. C2×#11924003 | C2×C4 | semidirect |
| 59. #14556525 | C2×C4 | semidirect |
| 62. C2×C16×C73 | C2×C4 | semidirect |
| 63. #107×C73 | C2×C4 | semidirect |
| 93. D584 | C4⋊C4 | semidirect |
| 106. D8×C73 | C4⋊C4 | semidirect |
| 197. C73 | #12937 | semidirect |
| 215. #357 | #64408 | semidirect |
| 242. C2×C16 | C2×#64408 | semidirect |
| 249. #107 | C2×#64408 | semidirect |
| 276. D8 | C4⋊#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×#64408 | 2 |
| C2×#17989514 | 2 |
| C2×#17989499 | 2 |
| #22626035 | 2 |
| #22624988 | 2 |
| #22624968 | 2 |
| #357×D73 | 2 |
| #12937 | 73 |