Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
222 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 88 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#432 | C2 | semidirect |
| 3. C23×#382 | C2 | semidirect |
| 4. C23×#328 | C2 | semidirect |
| 7. C23×#125 | C4 | semidirect |
| 8. C23×#124 | C4 | semidirect |
| 12. C4×Q8×C23 | C4 | semidirect |
| 14. C4×D4×C23 | C4 | semidirect |
| 73. #1512 | C23 | direct (N × H) |
| 93. #432 | C2×C23 | semidirect |
| 94. #382 | C2×C23 | semidirect |
| 95. #328 | C2×C23 | semidirect |
| 104. #125 | C4×C23 | semidirect |
| 105. #124 | C4×C23 | semidirect |
| 109. C4×Q8 | C4×C23 | semidirect |
| 111. C4×D4 | C4×C23 | semidirect |
| 120. C23 | #1512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#529 | 2 |
| C23×#432 | 2 |
| C23×#382 | 2 |
| C23×#328 | 2 |
| C23×#327 | 2 |
| #1512 | 23 |