Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C73 | #327 |
| commutator | C2×C8 | C2×C8×C73 |
| Frattini, cosocle | C2×#97 | C22×C73 |
| socle | C2×C73 | #1270 |
| prime radical | C2×#135×C73 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C73 ◁ C22×C4×C73 ◁ C2×#97×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C73×#1375 | C2 | semidirect |
| 3. C73×#1281 | C2 | semidirect |
| 14. C2×Q16×C73 | C8 | semidirect |
| 16. C2×D8×C73 | C8 | semidirect |
| 101. #7109 | C73 | direct (N × H) |
| 108. #1375 | C2×C73 | semidirect |
| 109. #1281 | C2×C73 | semidirect |
| 110. C73 | #7109 | direct (N × H) |
| 121. C2×Q16 | C8×C73 | semidirect |
| 123. C2×D8 | C8×C73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#1975 | 2 |
| C73×#1375 | 2 |
| C73×#1281 | 2 |
| #7109 | 73 |