Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
454 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 94 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. #22626046 | C2 | semidirect |
| 3. #22625490 | C2 | semidirect |
| 5. #22624823 | C2 | semidirect |
| 6. #22624763 | C2 | semidirect |
| 127. D4×C73 | #108 | semidirect |
| 204. C73 | #8906 | semidirect |
| 327. D4 | #14556661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#11924038 | 2 |
| #22626046 | 2 |
| #22625490 | 2 |
| #22625257 | 2 |
| #22624823 | 2 |
| #22624763 | 2 |
| D4⋊C8×D73 | 2 |
| #8906 | 73 |