Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22626165 | C2 | semidirect |
| 2. #22625603 | C2 | semidirect |
| 3. #22624903 | C2 | semidirect |
| 4. #22624902 | C2 | semidirect |
| 12. C2×#14556614 | C4 | semidirect |
| 17. #17988840 | C4 | semidirect |
| 20. #17988622 | C4 | semidirect |
| 22. #470×C73 | C4 | semidirect |
| 38. C2×D584 | C2×C4 | semidirect |
| 55. #14556523 | C2×C4 | semidirect |
| 59. C2×Q16×C73 | C2×C4 | semidirect |
| 62. #106×C73 | C2×C4 | semidirect |
| 198. C73 | #11685 | semidirect |
| 205. #470 | #64408 | semidirect |
| 220. C2×Q16 | C2×#64408 | semidirect |
| 252. #106 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626165 | 2 |
| #22625603 | 2 |
| #22624903 | 2 |
| #22624902 | 2 |
| #22619542 | 2 |
| #11685 | 73 |