Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22627056 | C2 | semidirect |
| 4. M16×#10596842 | C2 | semidirect |
| 5. #22626943 | C2 | semidirect |
| 6. #22626938 | C2 | semidirect |
| 59. #14556508 | C8 | semidirect |
| 60. #14556507 | C8 | semidirect |
| 61. #14556507 | C8 | semidirect |
| 62. #100×C73 | C8 | semidirect |
| 189. C73 | #9550 | semidirect |
| 233. #100 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627056 | 2 |
| #22627051 | 2 |
| C2×D4⋊#10596842 | 2 |
| M16×#10596842 | 2 |
| #22626943 | 2 |
| #22626938 | 2 |
| #100×#64408 | 2 |
| #9550 | 73 |