Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
482 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #22627056 | C2 | semidirect |
| 4. #22626938 | C2 | semidirect |
| 44. #14556508 | C8 | semidirect |
| 45. #14556507 | C8 | semidirect |
| 46. #100×C73 | C8 | semidirect |
| 76. #11924012 | C2×C8 | semidirect |
| 80. M16×C73 | C2×C8 | semidirect |
| 145. C73 | #8835 | semidirect |
| 179. #100 | #10596842 | semidirect |
| 205. M16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627173 | 2 |
| #22627081 | 2 |
| #22627056 | 2 |
| #22626938 | 2 |
| #100×#64408 | 2 |
| #8835 | 73 |