Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1060 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. C2×#17988720 | C2 | semidirect |
| 2. #22613569 | C2 | semidirect |
| 3. #22610768 | C2 | semidirect |
| 4. #22609863 | C2 | semidirect |
| 5. #22608499 | C2 | semidirect |
| 6. #22607778 | C2 | semidirect |
| 7. C73×#3186 | C2 | semidirect |
| 55. C22⋊#10596831 | D4 | semidirect |
| 61. C22×D4×C73 | D4 | semidirect |
| 64. C22×C8×C73 | D4 | semidirect |
| 74. C2×C4⋊C4×C73 | D4 | semidirect |
| 113. C22⋊Dic73 | D8 | semidirect |
| 269. #3186 | D73 | semidirect |
| 276. C73 | #9946 | semidirect |
| 312. C22×D4 | C22⋊D73 | semidirect |
| 318. C22×C8 | C22⋊D73 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988720 | 2 |
| #22613569 | 2 |
| #22610768 | 2 |
| #22609863 | 2 |
| #22608499 | 2 |
| #22607778 | 2 |
| C73×#3186 | 2 |
| #9946 | 73 |