Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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 | C42 | C23×C23 |
| prime radical | C23×#547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#498 | C2 | semidirect |
| 3. C23×#474 | C2 | semidirect |
| 4. C23×#461 | C2 | semidirect |
| 5. C23×#332 | C2 | semidirect |
| 6. C23×D4⋊C8 | C2 | semidirect |
| 7. C23×D4⋊C8 | C2 | semidirect |
| 60. D4×C23 | SD16 | semidirect |
| 76. #1654 | C23 | direct (N × H) |
| 94. #498 | C2×C23 | semidirect |
| 95. #474 | C2×C23 | semidirect |
| 96. #461 | C2×C23 | semidirect |
| 97. #332 | C2×C23 | semidirect |
| 98. D4⋊C8 | C2×C23 | semidirect |
| 99. D4⋊C8 | C2×C23 | semidirect |
| 122. C23 | #1654 | direct (N × H) |
| 158. D4 | SD16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#547 | 2 |
| C23×#498 | 2 |
| C23×#474 | 2 |
| C23×#461 | 2 |
| C23×#332 | 2 |
| C23×D4⋊C8 | 2 |
| #1654 | 23 |