Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#484 | C2 | semidirect |
| 3. C23×#481 | C2 | semidirect |
| 4. C23×#399 | C2 | semidirect |
| 5. C23×#328 | C2 | semidirect |
| 6. C23×#327 | C2 | semidirect |
| 7. C23×#323 | C2 | semidirect |
| 86. #1618 | C23 | direct (N × H) |
| 109. #484 | C2×C23 | semidirect |
| 110. #481 | C2×C23 | semidirect |
| 111. #399 | C2×C23 | semidirect |
| 112. #328 | C2×C23 | semidirect |
| 113. #327 | C2×C23 | semidirect |
| 114. #323 | C2×C23 | semidirect |
| 141. C23 | #1618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#538 | 2 |
| C23×#484 | 2 |
| C23×#481 | 2 |
| C23×#399 | 2 |
| C23×#328 | 2 |
| C23×#327 | 2 |
| C23×#323 | 2 |
| #1618 | 23 |