Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
546 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 546 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 |
|---|---|---|
| 1. #41×#10596842 | C2 | semidirect |
| 2. #22627050 | C2 | semidirect |
| 3. C2×D4⋊#10596842 | C2 | semidirect |
| 4. #22627045 | C2 | semidirect |
| 5. #22626943 | C2 | semidirect |
| 6. #22626938 | C2 | semidirect |
| 78. #14556619 | C8 | semidirect |
| 80. #14556617 | C8 | semidirect |
| 81. #14556616 | C8 | semidirect |
| 86. AGL(1,ℤ/8)×C73 | C8 | semidirect |
| 132. C2×D292 | C2×C8 | semidirect |
| 148. #11924012 | C2×C8 | semidirect |
| 152. C2×D4×C73 | C2×C8 | semidirect |
| 155. M16×C73 | C2×C8 | semidirect |
| 263. C73 | #9095 | semidirect |
| 297. AGL(1,ℤ/8) | #10596842 | semidirect |
| 359. C2×D4 | C2×#10596842 | semidirect |
| 383. M16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10596842 | 2 |
| #22627050 | 2 |
| C2×D4⋊#10596842 | 2 |
| #22627045 | 2 |
| #22626943 | 2 |
| #22626938 | 2 |
| AGL(1,ℤ/8)×#64408 | 2 |
| #9095 | 73 |