Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
206 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | D16 |
| commutator | C16 | C22×C4×C73 |
| Frattini, cosocle | C2×C16 | C23×C73 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C22×C4×C73 ◁ C22×C8×C73 ◁ C22×C16×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C73×#1423 | C2 | direct (N × H) |
| 6. C2×C32×C73 | C4 | semidirect |
| 18. C32×C73 | C2×C4 | semidirect |
| 48. C2×#1423 | C73 | direct (N × H) |
| 49. C2×C73 | #1423 | direct (N × H) |
| 55. #1423 | C2×C73 | direct (N × H) |
| 56. C73 | C2×#1423 | direct (N × H) |
| 59. C2×C32 | C4×C73 | semidirect |
| 71. C32 | C2×C4×C73 | semidirect |
| 101. C2 | C73×#1423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C73 | 2 |
| C2×#366×C73 | 2 |
| C73×#1423 | 2 |
| C2×#1423 | 73 |