Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 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 | C2×C23 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C23×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#576 | C2 | semidirect |
| 2. C23×#509 | C2 | semidirect |
| 3. C2×C23×D16 | C2 | semidirect |
| 4. C23×#472 | C2 | semidirect |
| 5. C23×#361 | C2 | semidirect |
| 6. C23×#359 | C2 | semidirect |
| 7. C23×#350 | C2 | semidirect |
| 16. C2×D8×C23 | C22 | semidirect |
| 21. C23×M32 | C22 | semidirect |
| 22. C2×C16×C23 | C22 | semidirect |
| 23. C23×#108 | C22 | semidirect |
| 75. #2192 | C23 | direct (N × H) |
| 88. #576 | C2×C23 | semidirect |
| 89. #509 | C2×C23 | semidirect |
| 90. C2×D16 | C2×C23 | semidirect |
| 91. #472 | C2×C23 | semidirect |
| 92. #361 | C2×C23 | semidirect |
| 93. #359 | C2×C23 | semidirect |
| 94. #350 | C2×C23 | semidirect |
| 109. C2×D8 | C22×C23 | semidirect |
| 114. M32 | C22×C23 | semidirect |
| 115. C2×C16 | C22×C23 | semidirect |
| 116. #108 | C22×C23 | semidirect |
| 118. C23 | #2192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#576 | 2 |
| C23×#509 | 2 |
| C2×C23×D16 | 2 |
| C23×#472 | 2 |
| C23×#361 | 2 |
| C23×#359 | 2 |
| C23×#350 | 2 |
| #2192 | 23 |