Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
542 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 127 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. M16×#10596842 | C2 | semidirect |
| 4. #22626943 | C2 | semidirect |
| 41. #14556651 | C8 | semidirect |
| 46. #14556508 | C8 | semidirect |
| 47. #14556507 | C8 | semidirect |
| 48. #100×C73 | C8 | semidirect |
| 67. #11924037 | C2×C8 | semidirect |
| 79. #11924012 | C2×C8 | semidirect |
| 83. M16×C73 | C2×C8 | semidirect |
| 106. #10596842 | #100 | direct (N × H) |
| 149. C73 | C8×#100 | semidirect |
| 185. #100 | #10596842 | direct (N × H) |
| 211. M16 | C2×#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10596842 | 2 |
| #22627045 | 2 |
| M16×#10596842 | 2 |
| #22626943 | 2 |
| #100×#64408 | 2 |
| C8×#100 | 73 |