Finite Group DatabasebetaFinite Group DatabasebetaOrder 9472.
258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | #102 |
| commutator | C2×C8 | C2×C8×C37 |
| Frattini, cosocle | C2×C4×C8 | C22×C37 |
| socle | C22×C37 | D4⋊C8 |
| prime radical | C2×#135×C37 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C22×C8×C37 ◁ C2×C4×C8×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#1376 | C2 | semidirect |
| 3. C37×#1273 | C2 | semidirect |
| 14. C2×Q16×C37 | C8 | semidirect |
| 16. C2×D8×C37 | C8 | semidirect |
| 91. #7114 | C37 | direct (N × H) |
| 108. #1376 | C2×C37 | semidirect |
| 109. #1273 | C2×C37 | semidirect |
| 123. C37 | #7114 | direct (N × H) |
| 127. C2×Q16 | C8×C37 | semidirect |
| 129. C2×D8 | C8×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#1974 | 2 |
| C37×#1376 | 2 |
| C37×#1273 | 2 |
| #7114 | 37 |