Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
612 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C22×#41×C23 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C23×#103 | C2 | semidirect |
| 3. C2×C23×#102 | C2 | semidirect |
| 4. C2×C23×C22⋊C8 | C2 | semidirect |
| 5. C23×#380 | C2 | semidirect |
| 9. C2×#41×C23 | C4 | semidirect |
| 66. Q8×C23 | C22⋊C4 | semidirect |
| 70. D4×C23 | C22⋊C4 | semidirect |
| 87. #1788 | C23 | direct (N × H) |
| 110. C2×#103 | C2×C23 | semidirect |
| 111. C2×#102 | C2×C23 | semidirect |
| 112. C2×C22⋊C8 | C2×C23 | semidirect |
| 113. #380 | C2×C23 | semidirect |
| 124. C2×#41 | C4×C23 | semidirect |
| 137. C23 | #1788 | direct (N × H) |
| 182. Q8 | C22⋊C4×C23 | semidirect |
| 186. D4 | C22⋊C4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C23 | 2 |
| C2×C23×#103 | 2 |
| C2×C23×#102 | 2 |
| C2×C23×C22⋊C8 | 2 |
| C23×#380 | 2 |
| #1788 | 23 |